0.11/0.23	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.24	% Command    : run_vampire %s %d
0.14/0.46	% Computer   : n008.cluster.edu
0.14/0.46	% Model      : x86_64 x86_64
0.14/0.46	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.46	% Memory     : 8042.1875MB
0.14/0.46	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.46	% CPULimit   : 1200
0.14/0.46	% WCLimit    : 120
0.14/0.46	% DateTime   : Tue Jul 13 10:39:29 EDT 2021
0.14/0.46	% CPUTime    : 
0.14/0.47	This is a THF_ problem
0.14/0.47	Running vampire --ignore_missing on --mode casc_hol --cores 0 -t 120 /export/starexec/sandbox/benchmark/theBenchmark.p
0.14/0.47	Running in auto input_syntax mode. Trying TPTP
0.14/0.54	% (13307)dis+1010_3:2_av=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark
0.14/0.54	% (13308)dis+1_2:3_acc=on:add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=2.0:amm=sco:anc=none:er=filter:fsr=off:gsp=input_only:gs=on:gsem=off:nm=64:newcnf=on:nwc=1:thsq=on_3 on theBenchmark
0.14/0.54	% (13305)lrs+1011_5:1_acc=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_3 on theBenchmark
0.14/0.54	% (13310)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on:thsq=on_2 on theBenchmark
0.14/0.54	% (13304)ott+1002_8:1_add=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=100000:afq=1.1:amm=off:anc=none:bd=off:bs=unit_only:fsr=off:gs=on:gsem=off:nm=32:nwc=10:sp=occurrence:urr=on:updr=off:thsq=on_14 on theBenchmark
0.14/0.56	% (13302)dis+10_128_acc=on:add=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on:thsq=on_2 on theBenchmark
0.14/0.56	% (13299)ott+1002_2_av=off:bd=preordered:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:irw=on:lma=on:nm=64:nwc=10:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark
0.14/0.56	% (13300)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_2 on theBenchmark
0.14/0.56	% (13303)lrs+1010_8_add=off:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on:thsq=on_13 on theBenchmark
0.14/0.56	% (13322)lrs+1002_1_add=large:csup=on:inj=on:fe=off:chr=on:cases=on:cnfonf=eager:afr=on:afp=1000:afq=1.1:amm=sco:anc=none:er=known:fsr=off:gs=on:gsem=off:lma=on:nm=2:newcnf=on:nwc=2:stl=30:sd=1:ss=axioms:st=5.0:sp=reverse_arity:updr=off:thsq=on_50 on theBenchmark
0.14/0.56	% (13328)dis-11_3_add=off:afp=40000:csup=on:inj=on:chr=on:e2e=on:prag=on:cases=on:cnfonf=eager:afq=1.0:fde=all:amm=sco:anc=none:gs=on:irw=on:lcm=reverse:nm=6:nwc=1:sd=4:ss=axioms:st=3.0:sos=on:sac=on:thsq=on_50 on theBenchmark
0.14/0.57	% (13314)ott+2_2_afp=10000:afq=1.4:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:amm=off:anc=none:gsp=input_only:gs=on:gsem=off:irw=on:lcm=predicate:nm=32:nwc=1.5:sos=on:sp=reverse_arity:thsq=on_7 on theBenchmark
0.14/0.57	% (13321)dis+10_4_av=off:bsr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:cond=fast:er=filter:fde=none:gsp=input_only:lcm=reverse:lma=on:nwc=4:sp=occurrence:urr=on:thsq=on_8 on theBenchmark
0.14/0.57	% (13301)lrs+1011_8_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_3 on theBenchmark
0.14/0.57	% (13313)lrs+1002_1_av=off:er=filter:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:fsr=off:gs=on:gsem=off:irw=on:lma=on:nm=4:nwc=1:stl=30:sd=3:ss=axioms:st=1.5:sos=on:thsq=on_1 on theBenchmark
0.14/0.57	% (13327)dis+1002_4_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=1.0:anc=none:cond=fast:fde=none:gs=on:gsaa=full_model:lma=on:lwlo=on:nm=0:nwc=1.5:sp=reverse_arity:tha=off_300 on theBenchmark
0.14/0.57	% (13320)lrs-11_4:1_afp=4000:csup=on:inj=on:chr=on:cases=on:cnfonf=lazy_gen:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_30 on theBenchmark
0.14/0.58	% (13306)lrs+4_3_av=off:br=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on:thsq=on_32 on theBenchmark
0.14/0.58	% (13326)lrs-11_4:1_afp=4000:csup=on:inj=on:mXXn=1:cases=on:e2e=on:cnfonf=eager:afq=2.0:anc=none:br=off:gs=on:lwlo=on:nm=64:nwc=3:stl=30:urr=on:thsq=on_186 on theBenchmark
0.14/0.58	% (13319)lrs+10_12_add=off:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.4:amm=sco:anc=none:cond=on:lma=on:nm=64:nwc=1.3:stl=30:sac=on:urr=on:thsq=on_41 on theBenchmark
0.14/0.58	% (13309)dis+10_128_acc=on:add=off:add=off:afp=4000:afq=1.4:amm=off:bd=preordered:cond=on:fsr=off:fde=unused:gs=on:gsem=on:irw=on:lma=on:nm=64:nwc=1.2:nicw=on:sos=on:sp=occurrence:updr=off:uhcvi=on:thsq=on_40 on theBenchmark
0.14/0.58	% (13324)lrs+1010_8_add=off:afp=100000:csup=on:inj=off:cases=on:chr=off:e2e=on:cnfonf=eager:afq=1.0:amm=off:anc=none:irw=on:nm=16:newcnf=on:nwc=1.1:nicw=on:stl=30:sp=reverse_arity:urr=on:thsq=on_13 on theBenchmark
0.14/0.58	% (13323)lrs+1011_5_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=1000:afq=1.2:anc=none:fsr=off:irw=on:lma=on:nm=64:newcnf=on:nwc=1:stl=30:sd=3:ss=axioms:st=2.0:sos=on:sac=on:sp=reverse_arity:urr=on:updr=off:thsq=on_130 on theBenchmark
0.14/0.58	% (13312)lrs+1010_3_av=off:fsr=off:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:gs=on:gsem=off:nm=2:newcnf=on:nwc=2:stl=30:sp=reverse_arity:urr=on:updr=off:thsq=on_9 on theBenchmark
0.14/0.58	% (13311)dis+1002_6_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=40000:afq=2.0:bsr=on:cond=on:irw=on:lma=on:nm=2:nwc=2.5:nicw=on:sp=reverse_arity:updr=off:thsq=on_2 on theBenchmark
0.14/0.58	% (13315)lrs+1010_3:2_afr=on:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:anc=none:gsp=input_only:irw=on:lwlo=on:nm=2:newcnf=on:nwc=1.7:sac=on:sp=occurrence:thsq=on_300 on theBenchmark
0.14/0.59	% (13305)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.59	% (13318)dis+1002_3:1_acc=model:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=40000:afq=1.1:anc=none:ccuc=first:fsr=off:gsp=input_only:irw=on:nm=16:nwc=1:sos=all:thsq=on_8 on theBenchmark
0.14/0.60	% (13316)lrs+1011_5:1_acc=on:csup=on:inj=on:e2e=on:prag=on:cases=on:cnfonf=eager:amm=off:anc=all_dependent:bd=off:ccuc=small_ones:fde=unused:gs=on:gsaa=full_model:gsem=off:lcm=predicate:lwlo=on:nm=6:newcnf=on:nwc=2.5:stl=30:sp=occurrence:updr=off:thsq=on_30 on theBenchmark
0.14/0.60	% (13317)ott+11_20_afr=on:afp=100000:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afq=1.0:amm=sco:anc=all:bsr=on:irw=on:lma=on:nm=4:nwc=1.2:sac=on:sp=occurrence:thsq=on_6 on theBenchmark
0.14/0.61	% (13325)lrs+1_4_afp=100000:afq=1.2:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:anc=none:bd=off:cond=on:gs=on:gsem=off:nm=64:nwc=1:sd=2:ss=axioms:st=2.0:sos=all:updr=off:thsq=on_300 on theBenchmark
0.14/0.62	% (13303)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.62	% (13308)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.62	% (13306)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.64	% (13321)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.14/0.64	% (13324)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.64	% (13307)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.14/0.64	% (13312)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.64	% (13322)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.14/0.64	% (13315)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.66/0.65	% (13316)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.66/0.65	% (13323)WARNING: Not using newCnf currently not compatible with polymorphic/higher-order inputs.
0.66/0.65	% (13314)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.66/0.66	% (13301)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.66/0.67	% (13308)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.66/0.67	% (13315)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
0.66/0.67	% (13318)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
1.51/0.74	% (13309)Refutation not found, incomplete strategy% (13309)------------------------------
1.51/0.74	% (13309)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
1.51/0.74	% (13309)Termination reason: Refutation not found, incomplete strategy
1.51/0.74	
1.51/0.74	% (13309)Memory used [KB]: 12281
1.51/0.74	% (13309)Time elapsed: 0.227 s
1.51/0.74	% (13309)------------------------------
1.51/0.74	% (13309)------------------------------
1.51/0.75	% (13302)Refutation not found, incomplete strategy% (13302)------------------------------
1.51/0.75	% (13302)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
1.51/0.75	% (13302)Termination reason: Refutation not found, incomplete strategy
1.51/0.75	
1.51/0.75	% (13302)Memory used [KB]: 11897
1.51/0.75	% (13302)Time elapsed: 0.235 s
1.51/0.75	% (13302)------------------------------
1.51/0.75	% (13302)------------------------------
2.00/0.76	% (13301)Refutation not found, incomplete strategy% (13301)------------------------------
2.00/0.76	% (13301)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
2.09/0.77	% (13301)Termination reason: Refutation not found, incomplete strategy
2.09/0.77	
2.09/0.77	% (13301)Memory used [KB]: 11513
2.09/0.77	% (13301)Time elapsed: 0.245 s
2.09/0.77	% (13301)------------------------------
2.09/0.77	% (13301)------------------------------
2.09/0.79	% (13334)dis+1011_10_add=large:csup=on:inj=on:chr=on:cases=on:cnfonf=eager:afr=on:afp=4000:afq=1.0:amm=off:anc=none:lma=on:nm=64:nwc=4:sac=on:sp=occurrence:thsq=on_75 on theBenchmark
2.09/0.80	% (13336)lrs+1011_8_add=large:csup=on:inj=on:prag=on:cases=on:cnfonf=eager:afp=100000:afq=1.1:er=filter:gsp=input_only:gs=on:gsem=on:lma=on:nm=6:nwc=1:stl=30:sd=2:ss=axioms:st=1.5:sos=on:thsq=on_26 on theBenchmark
2.41/0.81	% (13335)dis+1010_3:2_av=off:csup=on:prag=on:chr=on:cases=on:bet=on:cnfonf=lazy_not_be_gen:gsp=input_only:nm=2:nwc=1:sp=reverse_arity:urr=ec_only:thsq=on_29 on theBenchmark
2.41/0.83	% (13300)First to succeed.
2.65/0.85	% (13328)Refutation not found, incomplete strategy% (13328)------------------------------
2.65/0.85	% (13328)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
2.65/0.85	% (13328)Termination reason: Refutation not found, incomplete strategy
2.65/0.85	
2.65/0.85	% (13328)Memory used [KB]: 11897
2.65/0.85	% (13328)Time elapsed: 0.336 s
2.65/0.85	% (13328)------------------------------
2.65/0.85	% (13328)------------------------------
2.65/0.85	% (13323)Refutation not found, incomplete strategy% (13323)------------------------------
2.65/0.85	% (13323)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
2.65/0.85	% (13323)Termination reason: Refutation not found, incomplete strategy
2.65/0.85	
2.65/0.85	% (13323)Memory used [KB]: 7291
2.65/0.85	% (13323)Time elapsed: 0.323 s
2.65/0.85	% (13323)------------------------------
2.65/0.85	% (13323)------------------------------
2.65/0.86	% (13300)Refutation found. Thanks to Tanya!
2.65/0.86	% SZS status Theorem for theBenchmark
2.65/0.86	% SZS output start Proof for theBenchmark
2.65/0.86	thf(type_def_6, type, partia1833973666xt_a_b: $tType).
2.65/0.86	thf(type_def_7, type, product_prod_a_a: $tType).
2.65/0.86	thf(type_def_8, type, set_a: $tType).
2.65/0.86	thf(type_def_9, type, int: $tType).
2.65/0.86	thf(type_def_10, type, a: $tType).
2.65/0.86	thf(type_def_11, type, >: ($tType * $tType) > $tType).
2.65/0.86	thf(func_def_12, type, a_l_coset_a_b: partia1833973666xt_a_b > a > set_a > set_a).
2.65/0.86	thf(func_def_13, type, additi2104487374up_a_b: set_a > partia1833973666xt_a_b > $o).
2.65/0.86	thf(func_def_14, type, set_add_a_b: partia1833973666xt_a_b > set_a > set_a > set_a).
2.65/0.86	thf(func_def_15, type, partia1066395285xt_a_b: partia1833973666xt_a_b > set_a).
2.65/0.86	thf(func_def_16, type, mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a).
2.65/0.86	thf(func_def_17, type, minus_minus_int: int > int > int).
2.65/0.86	thf(func_def_18, type, minus_minus_set_a: set_a > set_a > set_a).
2.65/0.86	thf(func_def_19, type, plus_plus_int: int > int > int).
2.65/0.86	thf(func_def_20, type, uminus_uminus_int: int > int).
2.65/0.86	thf(func_def_21, type, uminus_uminus_set_a: set_a > set_a).
2.65/0.86	thf(func_def_22, type, locali1648887798ac_a_b: partia1833973666xt_a_b > set_a > $o).
2.65/0.86	thf(func_def_23, type, locali807230110ng_a_b: partia1833973666xt_a_b > set_a > $o).
2.65/0.86	thf(func_def_24, type, locali880295127ng_a_b: partia1833973666xt_a_b > set_a > $o).
2.65/0.86	thf(func_def_25, type, locali425460998xt_a_b: partia1833973666xt_a_b > set_a > $o).
2.65/0.86	thf(func_def_26, type, bot_bot_set_a: set_a).
2.65/0.86	thf(func_def_27, type, ord_less_eq_int: int > int > $o).
2.65/0.86	thf(func_def_28, type, ord_less_eq_set_a: set_a > set_a > $o).
2.65/0.86	thf(func_def_29, type, product_fst_a_a: product_prod_a_a > a).
2.65/0.86	thf(func_def_30, type, product_snd_a_a: product_prod_a_a > a).
2.65/0.86	thf(func_def_31, type, a_inv_a_b: partia1833973666xt_a_b > a > a).
2.65/0.86	thf(func_def_32, type, a_minus_a_b: partia1833973666xt_a_b > a > a > a).
2.65/0.86	thf(func_def_33, type, add_pow_a_b_int: partia1833973666xt_a_b > int > a > a).
2.65/0.86	thf(func_def_34, type, add_a_b: partia1833973666xt_a_b > a > a > a).
2.65/0.86	thf(func_def_35, type, zero_a_b: partia1833973666xt_a_b > a).
2.65/0.86	thf(func_def_36, type, semiring_a_b: partia1833973666xt_a_b > $o).
2.65/0.86	thf(func_def_37, type, collect_a: (a > $o) > set_a).
2.65/0.86	thf(func_def_38, type, member_a: a > set_a > $o).
2.65/0.86	thf(func_def_39, type, r: partia1833973666xt_a_b).
2.65/0.86	thf(func_def_40, type, s: set_a).
2.65/0.86	thf(func_def_41, type, r2: a).
2.65/0.86	thf(func_def_42, type, r3: a).
2.65/0.86	thf(func_def_43, type, s2: a).
2.65/0.86	thf(func_def_44, type, s3: a).
2.65/0.86	thf(func_def_45, type, t: a).
2.65/0.86	thf(func_def_46, type, t2: a).
2.65/0.86	thf(func_def_47, type, x: product_prod_a_a).
2.65/0.86	thf(func_def_48, type, y: product_prod_a_a).
2.65/0.86	thf(func_def_50, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
2.65/0.86	thf(func_def_53, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
2.65/0.86	thf(func_def_54, type, vAND: $o > $o > $o).
2.65/0.86	thf(func_def_55, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
2.65/0.86	thf(func_def_56, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
2.65/0.86	thf(func_def_57, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
2.65/0.86	thf(func_def_58, type, vIMP: $o > $o > $o).
2.65/0.86	thf(func_def_59, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
2.65/0.86	thf(func_def_60, type, vNOT: $o > $o).
2.65/0.86	thf(func_def_61, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
2.65/0.86	thf(func_def_62, type, sK0: a).
2.65/0.86	thf(func_def_63, type, sK1: a).
2.65/0.86	thf(func_def_64, type, sK2: set_a > a).
2.65/0.86	thf(func_def_65, type, sK3: set_a > a).
2.65/0.86	thf(func_def_66, type, sK4: set_a > a).
2.65/0.86	thf(func_def_67, type, sK5: set_a > a).
2.65/0.86	thf(func_def_68, type, sK6: a > a).
2.65/0.86	thf(func_def_69, type, sK7: a > a).
2.65/0.86	thf(func_def_70, type, sK8: a > a).
2.65/0.86	thf(func_def_71, type, sK9: (a > $o) > (a > $o) > a).
2.65/0.86	thf(func_def_72, type, sK10: set_a > set_a > a).
2.65/0.86	thf(func_def_73, type, sK11: (a > a > $o) > a).
2.65/0.86	thf(func_def_74, type, sK12: (a > a > $o) > a).
2.65/0.86	thf(func_def_76, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
2.65/0.86	thf(func_def_77, type, vOR: $o > $o > $o).
2.65/0.86	thf(func_def_78, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
2.65/0.86	thf(func_def_79, type, sK14: set_a > a).
2.65/0.86	thf(func_def_80, type, sK15: set_a > set_a > a).
2.65/0.86	thf(func_def_81, type, sK16: set_a > set_a > a).
2.65/0.86	thf(func_def_82, type, sK17: set_a > a).
2.65/0.86	thf(func_def_83, type, sK18: set_a > a).
2.65/0.86	thf(func_def_84, type, sK19: set_a > a).
2.65/0.86	thf(func_def_85, type, sK20: set_a > a).
2.65/0.86	thf(func_def_86, type, sK21: set_a > a).
2.65/0.86	thf(func_def_87, type, sK22: set_a > a).
2.65/0.86	thf(func_def_88, type, sK23: set_a > a).
2.65/0.86	thf(func_def_89, type, sK24: set_a > set_a > a).
2.65/0.86	thf(func_def_90, type, sK25: set_a > set_a > a).
2.65/0.86	thf(func_def_91, type, sK26: set_a > set_a > a).
2.65/0.86	thf(func_def_92, type, sK27: set_a > set_a > a).
2.65/0.86	thf(func_def_93, type, sK28: set_a > set_a > a).
2.65/0.86	thf(func_def_94, type, sK29: set_a > set_a > a).
2.65/0.86	thf(func_def_95, type, sK30: set_a > set_a > a).
2.65/0.86	thf(func_def_96, type, sK31: set_a > a).
2.65/0.86	thf(func_def_97, type, sK32: set_a > a).
2.65/0.86	thf(func_def_98, type, sK33: set_a > a).
2.65/0.86	thf(func_def_99, type, sK34: set_a > a).
2.65/0.86	thf(func_def_100, type, sK35: set_a > a).
2.65/0.86	thf(func_def_101, type, sK36: set_a > a).
2.65/0.86	thf(func_def_102, type, sK37: set_a > a).
2.65/0.86	thf(func_def_103, type, sK38: set_a > a).
2.65/0.86	thf(func_def_104, type, sK39: set_a > a).
2.65/0.86	thf(func_def_105, type, sK40: set_a > a).
2.65/0.86	thf(func_def_106, type, sK41: (a > $o) > a).
2.65/0.86	thf(func_def_107, type, sK42: (a > $o) > a).
2.65/0.86	thf(func_def_111, type, inv_uminus_uminus_int_43: int > int).
2.65/0.86	thf(f1827,plain,(
2.65/0.86	  $false),
2.65/0.86	  inference(avatar_sat_refutation,[],[f1691,f1701,f1703,f1826])).
2.65/0.86	thf(f1826,plain,(
2.65/0.86	  spl13_3),
2.65/0.86	  inference(avatar_contradiction_clause,[],[f1825])).
2.65/0.86	thf(f1825,plain,(
2.65/0.86	  $false | spl13_3),
2.65/0.86	  inference(trivial_inequality_removal,[],[f1824])).
2.65/0.86	thf(f1824,plain,(
2.65/0.86	  ($true = $false) | spl13_3),
2.65/0.86	  inference(backward_demodulation,[],[f1104,f1821])).
2.65/0.86	thf(f1821,plain,(
2.65/0.86	  (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ s) = $false) | spl13_3),
2.65/0.86	  inference(unit_resulting_resolution,[],[f1690,f1234])).
2.65/0.86	thf(f1234,plain,(
2.65/0.86	  ( ! [X1 : a] : ((((member_a @ X1) @ (partia1066395285xt_a_b @ r)) = $true) | (((member_a @ X1) @ s) = $false)) )),
2.65/0.86	  inference(binary_proxy_clausification,[],[f1233])).
2.65/0.86	thf(f1233,plain,(
2.65/0.86	  ( ! [X1 : a] : (($true = ((vIMP @ ((member_a @ X1) @ s)) @ ((member_a @ X1) @ (partia1066395285xt_a_b @ r))))) )),
2.65/0.86	  inference(combinator_demodulation,[],[f1232])).
2.65/0.86	thf(f1232,plain,(
2.65/0.86	  ( ! [X1 : a] : (($true = (((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ member_a) @ s))) @ ((cCOMB @ member_a) @ (partia1066395285xt_a_b @ r))) @ X1))) )),
2.65/0.86	  inference(pi_clausification,[],[f1231])).
2.65/0.86	thf(f1231,plain,(
2.65/0.86	  ($true = (vPI(a) @ ((sCOMB @ ((bCOMB @ vIMP) @ ((cCOMB @ member_a) @ s))) @ ((cCOMB @ member_a) @ (partia1066395285xt_a_b @ r)))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1204])).
2.65/0.86	thf(f1204,plain,(
2.65/0.86	  ($true = ((((bCOMB @ (bCOMB @ vPI(a))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ member_a))))) @ (cCOMB @ member_a))) @ s) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(definition_unfolding,[],[f1096,f889])).
2.65/0.86	thf(f889,plain,(
2.65/0.86	  (ord_less_eq_set_a = ((bCOMB @ (bCOMB @ vPI(a))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ member_a))))) @ (cCOMB @ member_a))))),
2.65/0.86	  inference(cnf_transformation,[],[f251])).
2.65/0.86	thf(f251,plain,(
2.65/0.86	  (ord_less_eq_set_a = ((bCOMB @ (bCOMB @ vPI(a))) @ ((cCOMB @ ((bCOMB @ bCOMB) @ ((bCOMB @ sCOMB) @ ((bCOMB @ (bCOMB @ vIMP)) @ (cCOMB @ member_a))))) @ (cCOMB @ member_a))))),
2.65/0.86	  inference(fool_elimination,[],[f250])).
2.65/0.86	thf(f250,plain,(
2.65/0.86	  (ord_less_eq_set_a = (^[X0 : set_a, X1 : set_a] : (! [X2 : a] : (((member_a @ X2) @ X0) => ((member_a @ X2) @ X1)))))),
2.65/0.86	  inference(rectify,[],[f121])).
2.65/0.86	thf(f121,axiom,(
2.65/0.86	  (ord_less_eq_set_a = (^[X28 : set_a, X29 : set_a] : (! [X20 : a] : (((member_a @ X20) @ X28) => ((member_a @ X20) @ X29)))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_subset__eq)).
2.65/0.86	thf(f1096,plain,(
2.65/0.86	  (((ord_less_eq_set_a @ s) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  inference(cnf_transformation,[],[f535])).
2.65/0.86	thf(f535,plain,(
2.65/0.86	  (((ord_less_eq_set_a @ s) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  inference(fool_elimination,[],[f534])).
2.65/0.86	thf(f534,plain,(
2.65/0.86	  ((ord_less_eq_set_a @ s) @ (partia1066395285xt_a_b @ r))),
2.65/0.86	  inference(rectify,[],[f231])).
2.65/0.86	thf(f231,axiom,(
2.65/0.86	  ((ord_less_eq_set_a @ s) @ (partia1066395285xt_a_b @ r))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_subset)).
2.65/0.86	thf(f1690,plain,(
2.65/0.86	  (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | spl13_3),
2.65/0.86	  inference(avatar_component_clause,[],[f1688])).
2.65/0.86	thf(f1688,plain,(
2.65/0.86	  spl13_3 <=> (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  introduced(avatar_definition,[new_symbols(naming,[spl13_3])])).
2.65/0.86	thf(f1104,plain,(
2.65/0.86	  (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ s) = $true)),
2.65/0.86	  inference(cnf_transformation,[],[f551])).
2.65/0.86	thf(f551,plain,(
2.65/0.86	  (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ s) = $true)),
2.65/0.86	  inference(fool_elimination,[],[f550])).
2.65/0.86	thf(f550,plain,(
2.65/0.86	  ((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ s)),
2.65/0.86	  inference(rectify,[],[f192])).
2.65/0.86	thf(f192,axiom,(
2.65/0.86	  ((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ s)),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_f8)).
2.65/0.86	thf(f1703,plain,(
2.65/0.86	  spl13_2),
2.65/0.86	  inference(avatar_contradiction_clause,[],[f1702])).
2.65/0.86	thf(f1702,plain,(
2.65/0.86	  $false | spl13_2),
2.65/0.86	  inference(subsumption_resolution,[],[f1686,f1230])).
2.65/0.86	thf(f1230,plain,(
2.65/0.86	  ($true = ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(combinator_demodulation,[],[f1205])).
2.65/0.86	thf(f1205,plain,(
2.65/0.86	  ($true = ((member_a @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(definition_unfolding,[],[f1116,f892])).
2.65/0.86	thf(f892,plain,(
2.65/0.86	  (a_minus_a_b = ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b))),
2.65/0.86	  inference(cnf_transformation,[],[f257])).
2.65/0.86	thf(f257,plain,(
2.65/0.86	  (a_minus_a_b = ((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b))),
2.65/0.86	  inference(fool_elimination,[],[f256])).
2.65/0.86	thf(f256,plain,(
2.65/0.86	  (a_minus_a_b = (^[X0 : partia1833973666xt_a_b, X1 : a, X2 : a] : ((((add_a_b @ X0) @ X1) @ ((a_inv_a_b @ X0) @ X2)))))),
2.65/0.86	  inference(rectify,[],[f171])).
2.65/0.86	thf(f171,axiom,(
2.65/0.86	  (a_minus_a_b = (^[X35 : partia1833973666xt_a_b, X20 : a, X36 : a] : ((((add_a_b @ X35) @ X20) @ ((a_inv_a_b @ X35) @ X36)))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_a__minus__def)).
2.65/0.86	thf(f1116,plain,(
2.65/0.86	  (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  inference(cnf_transformation,[],[f575])).
2.65/0.86	thf(f575,plain,(
2.65/0.86	  (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  inference(fool_elimination,[],[f574])).
2.65/0.86	thf(f574,plain,(
2.65/0.86	  ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))),
2.65/0.86	  inference(rectify,[],[f131])).
2.65/0.86	thf(f131,axiom,(
2.65/0.86	  ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_f42)).
2.65/0.86	thf(f1686,plain,(
2.65/0.86	  ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r))) | spl13_2),
2.65/0.86	  inference(avatar_component_clause,[],[f1684])).
2.65/0.86	thf(f1684,plain,(
2.65/0.86	  spl13_2 <=> ($true = ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  introduced(avatar_definition,[new_symbols(naming,[spl13_2])])).
2.65/0.86	thf(f1701,plain,(
2.65/0.86	  spl13_1),
2.65/0.86	  inference(avatar_contradiction_clause,[],[f1700])).
2.65/0.86	thf(f1700,plain,(
2.65/0.86	  $false | spl13_1),
2.65/0.86	  inference(subsumption_resolution,[],[f1682,f1229])).
2.65/0.86	thf(f1229,plain,(
2.65/0.86	  ($true = ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(combinator_demodulation,[],[f1206])).
2.65/0.86	thf(f1206,plain,(
2.65/0.86	  ($true = ((member_a @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(definition_unfolding,[],[f1117,f892])).
2.65/0.86	thf(f1117,plain,(
2.65/0.86	  (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  inference(cnf_transformation,[],[f577])).
2.65/0.86	thf(f577,plain,(
2.65/0.86	  (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) = $true)),
2.65/0.86	  inference(fool_elimination,[],[f576])).
2.65/0.86	thf(f576,plain,(
2.65/0.86	  ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r))),
2.65/0.86	  inference(rectify,[],[f29])).
2.65/0.86	thf(f29,axiom,(
2.65/0.86	  ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_f41)).
2.65/0.86	thf(f1682,plain,(
2.65/0.86	  ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r))) | spl13_1),
2.65/0.86	  inference(avatar_component_clause,[],[f1680])).
2.65/0.86	thf(f1680,plain,(
2.65/0.86	  spl13_1 <=> ($true = ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  introduced(avatar_definition,[new_symbols(naming,[spl13_1])])).
2.65/0.86	thf(f1691,plain,(
2.65/0.86	  ~spl13_1 | ~spl13_2 | ~spl13_3),
2.65/0.86	  inference(avatar_split_clause,[],[f1678,f1688,f1684,f1680])).
2.65/0.86	thf(f1678,plain,(
2.65/0.86	  (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r))) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(subsumption_resolution,[],[f1677,f1654])).
2.65/0.86	thf(f1654,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) != (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (zero_a_b @ r))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (zero_a_b @ r))))),
2.65/0.86	  inference(backward_demodulation,[],[f1653,f1650])).
2.65/0.86	thf(f1650,plain,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1123])).
2.65/0.86	thf(f1123,plain,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))),
2.65/0.86	  inference(definition_unfolding,[],[f868,f892])).
2.65/0.86	thf(f868,plain,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))),
2.65/0.86	  inference(cnf_transformation,[],[f126])).
2.65/0.86	thf(f126,axiom,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_f7)).
2.65/0.86	thf(f1653,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) != (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (zero_a_b @ r))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y))))))))),
2.65/0.86	  inference(backward_demodulation,[],[f1652,f1651])).
2.65/0.86	thf(f1651,plain,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t2) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1122])).
2.65/0.86	thf(f1122,plain,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t2) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))),
2.65/0.86	  inference(definition_unfolding,[],[f867,f892])).
2.65/0.86	thf(f867,plain,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))),
2.65/0.86	  inference(cnf_transformation,[],[f55])).
2.65/0.86	thf(f55,axiom,(
2.65/0.86	  ((zero_a_b @ r) = (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_f5)).
2.65/0.86	thf(f1652,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) != (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x))))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y))))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1121])).
2.65/0.86	thf(f1121,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) != (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  inference(definition_unfolding,[],[f864,f892,f892,f892,f892])).
2.65/0.86	thf(f864,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) != (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  inference(cnf_transformation,[],[f584])).
2.65/0.86	thf(f584,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) != (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  inference(flattening,[],[f34])).
2.65/0.86	thf(f34,negated_conjecture,(
2.65/0.86	  ~((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  inference(negated_conjecture,[],[f33])).
2.65/0.86	thf(f33,conjecture,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
2.65/0.86	thf(f1677,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (zero_a_b @ r))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (zero_a_b @ r)))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r))) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(forward_demodulation,[],[f1676,f1663])).
2.65/0.86	thf(f1663,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (zero_a_b @ r)))),
2.65/0.86	  inference(forward_demodulation,[],[f1643,f1658])).
2.65/0.86	thf(f1658,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (zero_a_b @ r)))),
2.65/0.86	  inference(forward_demodulation,[],[f1646,f1650])).
2.65/0.86	thf(f1646,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1127])).
2.65/0.86	thf(f1127,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y))))) = (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),
2.65/0.86	  inference(definition_unfolding,[],[f877,f892,f892])).
2.65/0.86	thf(f877,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y))))) = (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),
2.65/0.86	  inference(cnf_transformation,[],[f170])).
2.65/0.86	thf(f170,axiom,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ s2)) @ (product_snd_a_a @ x))) @ (((mult_a_ring_ext_a_b @ r) @ t) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ r3)) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ (product_fst_a_a @ y))))) = (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_f30)).
2.65/0.86	thf(f1643,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1130])).
2.65/0.86	thf(f1130,plain,(
2.65/0.86	  ((((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),
2.65/0.86	  inference(definition_unfolding,[],[f881,f892,f892])).
2.65/0.86	thf(f881,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) = (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),
2.65/0.86	  inference(cnf_transformation,[],[f183])).
2.65/0.86	thf(f183,axiom,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) = (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_f33)).
2.65/0.86	thf(f1676,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (zero_a_b @ r))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r))) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(forward_demodulation,[],[f1636,f1664])).
2.65/0.86	thf(f1664,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (zero_a_b @ r)))),
2.65/0.86	  inference(forward_demodulation,[],[f1642,f1659])).
2.65/0.86	thf(f1659,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (zero_a_b @ r)))),
2.65/0.86	  inference(forward_demodulation,[],[f1645,f1651])).
2.65/0.86	thf(f1645,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x)))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1128])).
2.65/0.86	thf(f1128,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x))))) = (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))),
2.65/0.86	  inference(definition_unfolding,[],[f878,f892,f892])).
2.65/0.86	thf(f878,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x))))) = (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))),
2.65/0.86	  inference(cnf_transformation,[],[f201])).
2.65/0.86	thf(f201,axiom,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t) @ s3)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ r2)) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ (product_fst_a_a @ x))))) = (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_f25)).
2.65/0.86	thf(f1642,plain,(
2.65/0.86	  ((((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))))),
2.65/0.86	  inference(combinator_demodulation,[],[f1131])).
2.65/0.86	thf(f1131,plain,(
2.65/0.86	  ((((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))),
2.65/0.86	  inference(definition_unfolding,[],[f882,f892,f892])).
2.65/0.86	thf(f882,plain,(
2.65/0.86	  ((((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))),
2.65/0.86	  inference(cnf_transformation,[],[f153])).
2.65/0.86	thf(f153,axiom,(
2.65/0.86	  ((((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2)))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) = (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_f32)).
2.65/0.86	thf(f1636,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) @ (partia1066395285xt_a_b @ r))) | ($true != ((member_a @ (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ ((a_inv_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(combinator_demodulation,[],[f1138])).
2.65/0.86	thf(f1138,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | ($true != ((member_a @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r))) | ($true != ((member_a @ (((((sCOMB @ ((bCOMB @ cCOMB) @ ((bCOMB @ (bCOMB @ bCOMB)) @ add_a_b))) @ a_inv_a_b) @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)))),
2.65/0.86	  inference(definition_unfolding,[],[f894,f892,f892,f892,f892,f892,f892])).
2.65/0.86	thf(f894,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) != $true) | (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) != $true)),
2.65/0.86	  inference(cnf_transformation,[],[f644])).
2.65/0.86	thf(f644,plain,(
2.65/0.86	  ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true) | (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) != $true) | (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) != $true)),
2.65/0.86	  inference(flattening,[],[f643])).
2.65/0.86	thf(f643,plain,(
2.65/0.86	  ((((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))))) | (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) != $true)) | (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) != $true)) | (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) != $true)),
2.65/0.86	  inference(ennf_transformation,[],[f261])).
2.65/0.86	thf(f261,plain,(
2.65/0.86	  (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) = $true) => ((((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) = $true) => ((((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) = $true) => ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))))),
2.65/0.86	  inference(fool_elimination,[],[f260])).
2.65/0.86	thf(f260,plain,(
2.65/0.86	  ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) => (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) => (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))))),
2.65/0.86	  inference(rectify,[],[f232])).
2.65/0.86	thf(f232,axiom,(
2.65/0.86	  ((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (partia1066395285xt_a_b @ r)) => (((member_a @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y))))) @ (partia1066395285xt_a_b @ r)) => (((member_a @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (partia1066395285xt_a_b @ r)) => ((((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((add_a_b @ r) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x))))) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))) = (((add_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s3) @ r2))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ y)) @ (product_fst_a_a @ x)))))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ t2) @ t)) @ (((a_minus_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_snd_a_a @ y))) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ r3))) @ (((mult_a_ring_ext_a_b @ r) @ (((mult_a_ring_ext_a_b @ r) @ s2) @ s3)) @ (((mult_a_ring_ext_a_b @ r) @ (product_snd_a_a @ x)) @ (product_fst_a_a @ y)))))))))),
2.65/0.86	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062)).
2.65/0.86	% SZS output end Proof for theBenchmark
2.65/0.86	% (13300)------------------------------
2.65/0.86	% (13300)Version: Vampire 4.6.0 (commit 0afb7ed4a on 2021-06-23 15:27:21 +0100)
2.65/0.86	% (13300)Termination reason: Refutation
2.65/0.86	
2.65/0.86	% (13300)Memory used [KB]: 12537
2.65/0.86	% (13300)Time elapsed: 0.328 s
2.65/0.86	% (13300)------------------------------
2.65/0.86	% (13300)------------------------------
2.65/0.86	% (13292)Success in time 0.382 s
2.65/0.86	EOF