0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : vampire --mode casc -t %d %s 0.13/0.34 % Computer : n013.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % DateTime : Thu Jul 2 09:06:04 EDT 2020 0.13/0.34 % CPUTime : 0.21/0.41 % dis+10_1_add=off:afp=4000:afq=1.2:anc=none:br=off:cond=on:gs=on:irw=on:lcm=reverse:nwc=10:sd=10:ss=axioms:sos=theory:sac=on:sp=occurrence:urr=on_2 on theBenchmark 0.21/0.42 % Refutation not found, incomplete strategy 0.21/0.42 % ------------------------------ 0.21/0.42 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 0.21/0.42 % Termination reason: Refutation not found, incomplete strategy 0.21/0.42 0.21/0.42 % Memory used [KB]: 9594 0.21/0.42 % Time elapsed: 0.003 s 0.21/0.42 % ------------------------------ 0.21/0.42 % ------------------------------ 0.21/0.48 % dis+10_3_add=large:afp=10000:afq=1.0:amm=sco:anc=none:gsp=input_only:gs=on:gsem=off:lcm=reverse:nwc=1:sos=on_6 on theBenchmark 0.21/0.48 % Refutation not found, incomplete strategy 0.21/0.48 % ------------------------------ 0.21/0.48 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 0.21/0.48 % Termination reason: Refutation not found, incomplete strategy 0.21/0.48 0.21/0.48 % Memory used [KB]: 9722 0.21/0.48 % Time elapsed: 0.003 s 0.21/0.48 % ------------------------------ 0.21/0.48 % ------------------------------ 0.21/0.52 % dis+11_1_acc=on:afp=1000:afq=1.4:amm=sco:anc=all_dependent:bs=on:ccuc=small_ones:cond=fast:fde=none:gsp=input_only:nm=64:nwc=1:sac=on:urr=ec_only:updr=off:uhcvi=on_105 on theBenchmark 14.24/14.32 % Time limit reached! 14.24/14.32 % ------------------------------ 14.24/14.32 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 14.24/14.32 % Termination reason: Time limit 14.24/14.32 % Termination phase: Saturation 14.24/14.32 14.24/14.32 % Memory used [KB]: 349631 14.24/14.32 % Time elapsed: 13.800 s 14.24/14.32 % ------------------------------ 14.24/14.32 % ------------------------------ 14.26/14.38 % lrs+11_20_av=off:bs=unit_only:bsr=on:bce=on:cond=on:fde=none:gs=on:gsem=on:irw=on:nm=4:nwc=1:stl=30:sos=theory:sp=reverse_arity:uhcvi=on_92 on theBenchmark 26.45/26.48 % Time limit reached! 26.45/26.48 % ------------------------------ 26.45/26.48 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 26.45/26.48 % Termination reason: Time limit 26.45/26.48 % Termination phase: Saturation 26.45/26.48 26.45/26.48 % Memory used [KB]: 177694 26.45/26.48 % Time elapsed: 12.100 s 26.45/26.48 % ------------------------------ 26.45/26.48 % ------------------------------ 26.53/26.53 % dis+1002_6_add=large: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_7 on theBenchmark 27.66/27.63 % Time limit reached! 27.66/27.63 % ------------------------------ 27.66/27.63 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 27.66/27.63 % Termination reason: Time limit 27.66/27.63 % Termination phase: Saturation 27.66/27.63 27.66/27.63 % Memory used [KB]: 48485 27.66/27.63 % Time elapsed: 1.100 s 27.66/27.63 % ------------------------------ 27.66/27.63 % ------------------------------ 27.66/27.67 % lrs+1_4:1_awrs=converge:awrsf=128:av=off:cond=fast:fde=none:gsp=input_only:gs=on:gsem=on:lcm=predicate:lwlo=on:nm=4:newcnf=on:nwc=1:stl=30:sd=3:ss=axioms:s2a=on:st=2.0:sos=on_27 on theBenchmark 27.66/27.67 % Refutation not found, incomplete strategy 27.66/27.67 % ------------------------------ 27.66/27.67 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 27.66/27.67 % Termination reason: Refutation not found, incomplete strategy 27.66/27.67 27.66/27.67 % Memory used [KB]: 5117 27.66/27.67 % Time elapsed: 0.002 s 27.66/27.67 % ------------------------------ 27.66/27.67 % ------------------------------ 27.72/27.70 % lrs+1011_8_add=large: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_3 on theBenchmark 27.72/27.70 % Refutation not found, incomplete strategy 27.72/27.70 % ------------------------------ 27.72/27.70 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 27.72/27.70 % Termination reason: Refutation not found, incomplete strategy 27.72/27.70 27.72/27.70 % Memory used [KB]: 9594 27.72/27.70 % Time elapsed: 0.002 s 27.72/27.70 % ------------------------------ 27.72/27.70 % ------------------------------ 27.72/27.74 % lrs+4_3_av=off:br=off:nm=0:newcnf=on:nwc=1:stl=30:sp=occurrence:urr=on_32 on theBenchmark 32.05/32.04 % Time limit reached! 32.05/32.04 % ------------------------------ 32.05/32.04 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 32.05/32.04 % Termination reason: Time limit 32.05/32.04 % Termination phase: Saturation 32.05/32.04 32.05/32.04 % Memory used [KB]: 87631 32.05/32.04 % Time elapsed: 4.300 s 32.05/32.04 % ------------------------------ 32.05/32.04 % ------------------------------ 32.05/32.08 % dis+1011_4_av=off:cond=on:irw=on:lma=on:nm=2:nwc=1:sos=all:sp=occurrence_5 on theBenchmark 33.06/32.98 % Time limit reached! 33.06/32.98 % ------------------------------ 33.06/32.98 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 33.06/32.98 % Termination reason: Time limit 33.06/32.98 % Termination phase: Saturation 33.06/32.98 33.06/32.98 % Memory used [KB]: 17654 33.06/32.98 % Time elapsed: 0.900 s 33.06/32.98 % ------------------------------ 33.06/32.98 % ------------------------------ 33.08/33.04 % lrs+1002_4:1_aac=none:add=off:afr=on:afp=40000:afq=1.0:amm=off:anc=none:cond=on:fsr=off:fde=none:gs=on:gsaa=full_model:lma=on:nm=16:nwc=1:sas=z3:stl=30:sd=7:ss=axioms:sos=on:sp=occurrence:updr=off:uhcvi=on_85 on theBenchmark 33.08/33.10 % Refutation not found, incomplete strategy 33.08/33.10 % ------------------------------ 33.08/33.10 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 33.08/33.10 % Termination reason: Refutation not found, incomplete strategy 33.08/33.10 33.08/33.10 % Memory used [KB]: 5117 33.08/33.10 % Time elapsed: 0.063 s 33.08/33.10 % ------------------------------ 33.08/33.10 % ------------------------------ 33.21/33.15 % lrs+1_5:1_afr=on:afp=100000:afq=2.0:amm=off:anc=none:bd=off:fde=none:gs=on:gsaa=full_model:gsem=on:irw=on:lwlo=on:nm=0:nwc=2.5:stl=30:sp=occurrence:uhcvi=on_42 on theBenchmark 38.89/38.75 % Time limit reached! 38.89/38.75 % ------------------------------ 38.89/38.75 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 38.89/38.75 % Termination reason: Time limit 38.89/38.75 % Termination phase: Saturation 38.89/38.75 38.89/38.75 % Memory used [KB]: 153899 38.89/38.75 % Time elapsed: 5.600 s 38.89/38.75 % ------------------------------ 38.89/38.75 % ------------------------------ 38.89/38.79 % lrs+1011_2:3_add=large:afr=on:afp=100000:afq=1.2:anc=none:gs=on:gsem=off:irw=on:nm=64:nwc=1:stl=30:sd=3:ss=axioms:sos=all:sp=reverse_arity_48 on theBenchmark 38.89/38.79 % Refutation not found, incomplete strategy 38.89/38.79 % ------------------------------ 38.89/38.79 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 38.89/38.79 % Termination reason: Refutation not found, incomplete strategy 38.89/38.79 38.89/38.79 % Memory used [KB]: 9594 38.89/38.79 % Time elapsed: 0.003 s 38.89/38.79 % ------------------------------ 38.89/38.79 % ------------------------------ 38.98/38.83 % ott+4_32_av=off:bsr=on:cond=on:er=known:fsr=off:gsp=input_only:gs=on:gsem=on:irw=on:lma=on:nm=4:nwc=1.2:sos=theory_197 on theBenchmark 45.33/45.19 % Refutation found. Thanks to Tanya! 45.33/45.19 % SZS status Theorem for theBenchmark 45.33/45.19 % SZS output start Proof for theBenchmark 45.33/45.19 fof(f179201,plain,( 45.33/45.19 $false), 45.33/45.19 inference(subsumption_resolution,[],[f178137,f178711])). 45.33/45.19 fof(f178711,plain,( 45.33/45.19 ( ! [X97] : (is_a_theorem(equiv(X97,X97))) )), 45.33/45.19 inference(resolution,[],[f178206,f482])). 45.33/45.19 fof(f482,plain,( 45.33/45.19 ( ! [X0] : (is_a_theorem(necessarily(or(X0,not(X0))))) )), 45.33/45.19 inference(backward_demodulation,[],[f479,f206])). 45.33/45.19 fof(f206,plain,( 45.33/45.19 ( ! [X0] : (is_a_theorem(necessarily(or(X0,and(not(X0),not(X0)))))) )), 45.33/45.19 inference(superposition,[],[f180,f186])). 45.33/45.19 fof(f186,plain,( 45.33/45.19 ( ! [X0,X1] : (necessarily(or(X0,X1)) = strict_implies(not(X0),X1)) )), 45.33/45.19 inference(superposition,[],[f168,f172])). 45.33/45.19 fof(f172,plain,( 45.33/45.19 ( ! [X0,X1] : (implies(not(X0),X1) = or(X0,X1)) )), 45.33/45.19 inference(global_subsumption,[],[f148,f171])). 45.33/45.19 fof(f171,plain,( 45.33/45.19 ( ! [X0,X1] : (implies(not(X0),X1) = or(X0,X1) | ~op_or) )), 45.33/45.19 inference(forward_demodulation,[],[f155,f169])). 45.33/45.19 fof(f169,plain,( 45.33/45.19 ( ! [X0,X1] : (implies(X0,X1) = not(and(X0,not(X1)))) )), 45.33/45.19 inference(global_subsumption,[],[f143,f153])). 45.33/45.19 fof(f153,plain,( 45.33/45.19 ( ! [X0,X1] : (implies(X0,X1) = not(and(X0,not(X1))) | ~op_implies_and) )), 45.33/45.19 inference(cnf_transformation,[],[f115])). 45.33/45.19 fof(f115,plain,( 45.33/45.19 ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) | ~op_implies_and), 45.33/45.19 inference(ennf_transformation,[],[f30])). 45.33/45.19 fof(f30,axiom,( 45.33/45.19 op_implies_and => ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_and)). 45.33/45.19 fof(f143,plain,( 45.33/45.19 op_implies_and), 45.33/45.19 inference(cnf_transformation,[],[f78])). 45.33/45.19 fof(f78,axiom,( 45.33/45.19 op_implies_and), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and)). 45.33/45.19 fof(f155,plain,( 45.33/45.19 ( ! [X0,X1] : (or(X0,X1) = not(and(not(X0),not(X1))) | ~op_or) )), 45.33/45.19 inference(cnf_transformation,[],[f117])). 45.33/45.19 fof(f117,plain,( 45.33/45.19 ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) | ~op_or), 45.33/45.19 inference(ennf_transformation,[],[f29])). 45.33/45.19 fof(f29,axiom,( 45.33/45.19 op_or => ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or)). 45.33/45.19 fof(f148,plain,( 45.33/45.19 op_or), 45.33/45.19 inference(cnf_transformation,[],[f77])). 45.33/45.19 fof(f77,axiom,( 45.33/45.19 op_or), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or)). 45.33/45.19 fof(f168,plain,( 45.33/45.19 ( ! [X0,X1] : (necessarily(implies(X0,X1)) = strict_implies(X0,X1)) )), 45.33/45.19 inference(global_subsumption,[],[f145,f152])). 45.33/45.19 fof(f152,plain,( 45.33/45.19 ( ! [X0,X1] : (necessarily(implies(X0,X1)) = strict_implies(X0,X1) | ~op_strict_implies) )), 45.33/45.19 inference(cnf_transformation,[],[f114])). 45.33/45.19 fof(f114,plain,( 45.33/45.19 ! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,X1) | ~op_strict_implies), 45.33/45.19 inference(ennf_transformation,[],[f56])). 45.33/45.19 fof(f56,axiom,( 45.33/45.19 op_strict_implies => ! [X0,X1] : necessarily(implies(X0,X1)) = strict_implies(X0,X1)), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies)). 45.33/45.19 fof(f145,plain,( 45.33/45.19 op_strict_implies), 45.33/45.19 inference(cnf_transformation,[],[f63])). 45.33/45.19 fof(f63,axiom,( 45.33/45.19 op_strict_implies), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies)). 45.33/45.19 fof(f180,plain,( 45.33/45.19 ( ! [X0] : (is_a_theorem(strict_implies(X0,and(X0,X0)))) )), 45.33/45.19 inference(global_subsumption,[],[f140,f163])). 45.33/45.19 fof(f163,plain,( 45.33/45.19 ( ! [X0] : (is_a_theorem(strict_implies(X0,and(X0,X0))) | ~axiom_m4) )), 45.33/45.19 inference(cnf_transformation,[],[f127])). 45.33/45.19 fof(f127,plain,( 45.33/45.19 ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) | ~axiom_m4), 45.33/45.19 inference(ennf_transformation,[],[f103])). 45.33/45.19 fof(f103,plain,( 45.33/45.19 axiom_m4 => ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f41])). 45.33/45.19 fof(f41,axiom,( 45.33/45.19 ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) <=> axiom_m4), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m4)). 45.33/45.19 fof(f140,plain,( 45.33/45.19 axiom_m4), 45.33/45.19 inference(cnf_transformation,[],[f71])). 45.33/45.19 fof(f71,axiom,( 45.33/45.19 axiom_m4), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4)). 45.33/45.19 fof(f479,plain,( 45.33/45.19 ( ! [X0] : (and(X0,X0) = X0) )), 45.33/45.19 inference(subsumption_resolution,[],[f398,f447])). 45.33/45.19 fof(f447,plain,( 45.33/45.19 ( ! [X2,X3] : (is_a_theorem(strict_implies(and(X3,X2),X2))) )), 45.33/45.19 inference(superposition,[],[f174,f417])). 45.33/45.19 fof(f417,plain,( 45.33/45.19 ( ! [X12,X11] : (and(X11,X12) = and(X12,X11)) )), 45.33/45.19 inference(global_subsumption,[],[f175,f405])). 45.33/45.19 fof(f405,plain,( 45.33/45.19 ( ! [X12,X11] : (~is_a_theorem(strict_implies(and(X11,X12),and(X12,X11))) | and(X11,X12) = and(X12,X11)) )), 45.33/45.19 inference(resolution,[],[f390,f175])). 45.33/45.19 fof(f390,plain,( 45.33/45.19 ( ! [X6,X7] : (~is_a_theorem(strict_implies(X7,X6)) | ~is_a_theorem(strict_implies(X6,X7)) | X6 = X7) )), 45.33/45.19 inference(resolution,[],[f220,f176])). 45.33/45.19 fof(f176,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(strict_equiv(X0,X1)) | X0 = X1) )), 45.33/45.19 inference(global_subsumption,[],[f142,f159])). 45.33/45.19 fof(f159,plain,( 45.33/45.19 ( ! [X0,X1] : (X0 = X1 | ~is_a_theorem(strict_equiv(X0,X1)) | ~substitution_strict_equiv) )), 45.33/45.19 inference(cnf_transformation,[],[f121])). 45.33/45.19 fof(f121,plain,( 45.33/45.19 ! [X0,X1] : (X0 = X1 | ~is_a_theorem(strict_equiv(X0,X1))) | ~substitution_strict_equiv), 45.33/45.19 inference(ennf_transformation,[],[f106])). 45.33/45.19 fof(f106,plain,( 45.33/45.19 substitution_strict_equiv => ! [X0,X1] : (is_a_theorem(strict_equiv(X0,X1)) => X0 = X1)), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f36])). 45.33/45.19 fof(f36,axiom,( 45.33/45.19 substitution_strict_equiv <=> ! [X0,X1] : (is_a_theorem(strict_equiv(X0,X1)) => X0 = X1)), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_strict_equiv)). 45.33/45.19 fof(f142,plain,( 45.33/45.19 substitution_strict_equiv), 45.33/45.19 inference(cnf_transformation,[],[f64])). 45.33/45.19 fof(f64,axiom,( 45.33/45.19 substitution_strict_equiv), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv)). 45.33/45.19 fof(f220,plain,( 45.33/45.19 ( ! [X4,X5] : (is_a_theorem(strict_equiv(X4,X5)) | ~is_a_theorem(strict_implies(X4,X5)) | ~is_a_theorem(strict_implies(X5,X4))) )), 45.33/45.19 inference(superposition,[],[f177,f170])). 45.33/45.19 fof(f170,plain,( 45.33/45.19 ( ! [X0,X1] : (and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1)) )), 45.33/45.19 inference(global_subsumption,[],[f144,f154])). 45.33/45.19 fof(f154,plain,( 45.33/45.19 ( ! [X0,X1] : (and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) | ~op_strict_equiv) )), 45.33/45.19 inference(cnf_transformation,[],[f116])). 45.33/45.19 fof(f116,plain,( 45.33/45.19 ! [X0,X1] : and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) | ~op_strict_equiv), 45.33/45.19 inference(ennf_transformation,[],[f58])). 45.33/45.19 fof(f58,axiom,( 45.33/45.19 op_strict_equiv => ! [X0,X1] : and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1)), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_equiv)). 45.33/45.19 fof(f144,plain,( 45.33/45.19 op_strict_equiv), 45.33/45.19 inference(cnf_transformation,[],[f72])). 45.33/45.19 fof(f72,axiom,( 45.33/45.19 op_strict_equiv), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv)). 45.33/45.19 fof(f177,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(and(X0,X1)) | ~is_a_theorem(X0) | ~is_a_theorem(X1)) )), 45.33/45.19 inference(global_subsumption,[],[f134,f160])). 45.33/45.19 fof(f160,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(and(X0,X1)) | ~is_a_theorem(X0) | ~is_a_theorem(X1) | ~adjunction) )), 45.33/45.19 inference(cnf_transformation,[],[f123])). 45.33/45.19 fof(f123,plain,( 45.33/45.19 ! [X0,X1] : (is_a_theorem(and(X0,X1)) | ~is_a_theorem(X0) | ~is_a_theorem(X1)) | ~adjunction), 45.33/45.19 inference(flattening,[],[f122])). 45.33/45.19 fof(f122,plain,( 45.33/45.19 ! [X0,X1] : (is_a_theorem(and(X0,X1)) | (~is_a_theorem(X0) | ~is_a_theorem(X1))) | ~adjunction), 45.33/45.19 inference(ennf_transformation,[],[f105])). 45.33/45.19 fof(f105,plain,( 45.33/45.19 adjunction => ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(X1)) => is_a_theorem(and(X0,X1)))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f37])). 45.33/45.19 fof(f37,axiom,( 45.33/45.19 adjunction <=> ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(X1)) => is_a_theorem(and(X0,X1)))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adjunction)). 45.33/45.19 fof(f134,plain,( 45.33/45.19 adjunction), 45.33/45.19 inference(cnf_transformation,[],[f60])). 45.33/45.19 fof(f60,axiom,( 45.33/45.19 adjunction), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction)). 45.33/45.19 fof(f175,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))) )), 45.33/45.19 inference(global_subsumption,[],[f137,f158])). 45.33/45.19 fof(f158,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) | ~axiom_m1) )), 45.33/45.19 inference(cnf_transformation,[],[f120])). 45.33/45.19 fof(f120,plain,( 45.33/45.19 ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) | ~axiom_m1), 45.33/45.19 inference(ennf_transformation,[],[f104])). 45.33/45.19 fof(f104,plain,( 45.33/45.19 axiom_m1 => ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f39])). 45.33/45.19 fof(f39,axiom,( 45.33/45.19 axiom_m1 <=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1)). 45.33/45.19 fof(f137,plain,( 45.33/45.19 axiom_m1), 45.33/45.19 inference(cnf_transformation,[],[f67])). 45.33/45.19 fof(f67,axiom,( 45.33/45.19 axiom_m1), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1)). 45.33/45.19 fof(f174,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),X0))) )), 45.33/45.19 inference(global_subsumption,[],[f136,f157])). 45.33/45.19 fof(f157,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(and(X0,X1),X0)) | ~axiom_m2) )), 45.33/45.19 inference(cnf_transformation,[],[f119])). 45.33/45.19 fof(f119,plain,( 45.33/45.19 ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) | ~axiom_m2), 45.33/45.19 inference(ennf_transformation,[],[f102])). 45.33/45.19 fof(f102,plain,( 45.33/45.19 axiom_m2 => ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f42])). 45.33/45.19 fof(f42,axiom,( 45.33/45.19 axiom_m2 <=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m2)). 45.33/45.19 fof(f136,plain,( 45.33/45.19 axiom_m2), 45.33/45.19 inference(cnf_transformation,[],[f65])). 45.33/45.19 fof(f65,axiom,( 45.33/45.19 axiom_m2), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2)). 45.33/45.19 fof(f398,plain,( 45.33/45.19 ( ! [X0] : (~is_a_theorem(strict_implies(and(X0,X0),X0)) | and(X0,X0) = X0) )), 45.33/45.19 inference(resolution,[],[f390,f180])). 45.33/45.19 fof(f178206,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(X0) | is_a_theorem(equiv(X1,X1))) )), 45.33/45.19 inference(forward_demodulation,[],[f178162,f437])). 45.33/45.19 fof(f437,plain,( 45.33/45.19 ( ! [X7] : (equiv(X7,X7) = implies(X7,X7)) )), 45.33/45.19 inference(subsumption_resolution,[],[f402,f424])). 45.33/45.19 fof(f424,plain,( 45.33/45.19 ( ! [X2,X3] : (is_a_theorem(strict_implies(equiv(X3,X2),implies(X2,X3)))) )), 45.33/45.19 inference(superposition,[],[f278,f415])). 45.33/45.19 fof(f415,plain,( 45.33/45.19 ( ! [X4,X3] : (equiv(X3,X4) = equiv(X4,X3)) )), 45.33/45.19 inference(global_subsumption,[],[f282,f400])). 45.33/45.19 fof(f400,plain,( 45.33/45.19 ( ! [X4,X3] : (~is_a_theorem(strict_implies(equiv(X3,X4),equiv(X4,X3))) | equiv(X3,X4) = equiv(X4,X3)) )), 45.33/45.19 inference(resolution,[],[f390,f282])). 45.33/45.19 fof(f282,plain,( 45.33/45.19 ( ! [X6,X7] : (is_a_theorem(strict_implies(equiv(X7,X6),equiv(X6,X7)))) )), 45.33/45.19 inference(forward_demodulation,[],[f276,f173])). 45.33/45.19 fof(f173,plain,( 45.33/45.19 ( ! [X0,X1] : (equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))) )), 45.33/45.19 inference(global_subsumption,[],[f147,f156])). 45.33/45.19 fof(f156,plain,( 45.33/45.19 ( ! [X0,X1] : (equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) | ~op_equiv) )), 45.33/45.19 inference(cnf_transformation,[],[f118])). 45.33/45.19 fof(f118,plain,( 45.33/45.19 ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) | ~op_equiv), 45.33/45.19 inference(ennf_transformation,[],[f28])). 45.33/45.19 fof(f28,axiom,( 45.33/45.19 op_equiv => ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv)). 45.33/45.19 fof(f147,plain,( 45.33/45.19 op_equiv), 45.33/45.19 inference(cnf_transformation,[],[f74])). 45.33/45.19 fof(f74,axiom,( 45.33/45.19 op_equiv), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv)). 45.33/45.19 fof(f276,plain,( 45.33/45.19 ( ! [X6,X7] : (is_a_theorem(strict_implies(and(implies(X7,X6),implies(X6,X7)),equiv(X6,X7)))) )), 45.33/45.19 inference(superposition,[],[f175,f173])). 45.33/45.19 fof(f278,plain,( 45.33/45.19 ( ! [X10,X11] : (is_a_theorem(strict_implies(equiv(X10,X11),implies(X10,X11)))) )), 45.33/45.19 inference(superposition,[],[f174,f173])). 45.33/45.19 fof(f402,plain,( 45.33/45.19 ( ! [X7] : (~is_a_theorem(strict_implies(equiv(X7,X7),implies(X7,X7))) | equiv(X7,X7) = implies(X7,X7)) )), 45.33/45.19 inference(resolution,[],[f390,f280])). 45.33/45.19 fof(f280,plain,( 45.33/45.19 ( ! [X13] : (is_a_theorem(strict_implies(implies(X13,X13),equiv(X13,X13)))) )), 45.33/45.19 inference(superposition,[],[f180,f173])). 45.33/45.19 fof(f178162,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(X0) | is_a_theorem(implies(X1,X1))) )), 45.33/45.19 inference(resolution,[],[f178100,f7883])). 45.33/45.19 fof(f7883,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (~is_a_theorem(strict_implies(X2,equiv(X1,X0))) | ~is_a_theorem(X2) | is_a_theorem(implies(X0,X1))) )), 45.33/45.19 inference(superposition,[],[f6150,f415])). 45.33/45.19 fof(f6150,plain,( 45.33/45.19 ( ! [X12,X10,X11] : (~is_a_theorem(strict_implies(X10,equiv(X11,X12))) | ~is_a_theorem(X10) | is_a_theorem(implies(X11,X12))) )), 45.33/45.19 inference(resolution,[],[f3164,f178])). 45.33/45.19 fof(f178,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(strict_implies(X0,X1)) | ~is_a_theorem(X0) | is_a_theorem(X1)) )), 45.33/45.19 inference(global_subsumption,[],[f139,f161])). 45.33/45.19 fof(f161,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(X0) | ~is_a_theorem(strict_implies(X0,X1)) | ~modus_ponens_strict_implies) )), 45.33/45.19 inference(cnf_transformation,[],[f125])). 45.33/45.19 fof(f125,plain,( 45.33/45.19 ! [X0,X1] : (is_a_theorem(X1) | ~is_a_theorem(X0) | ~is_a_theorem(strict_implies(X0,X1))) | ~modus_ponens_strict_implies), 45.33/45.19 inference(flattening,[],[f124])). 45.33/45.19 fof(f124,plain,( 45.33/45.19 ! [X0,X1] : (is_a_theorem(X1) | (~is_a_theorem(X0) | ~is_a_theorem(strict_implies(X0,X1)))) | ~modus_ponens_strict_implies), 45.33/45.19 inference(ennf_transformation,[],[f99])). 45.33/45.19 fof(f99,plain,( 45.33/45.19 modus_ponens_strict_implies => ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(strict_implies(X0,X1))) => is_a_theorem(X1))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f54])). 45.33/45.19 fof(f54,axiom,( 45.33/45.19 modus_ponens_strict_implies <=> ! [X0,X1] : ((is_a_theorem(X0) & is_a_theorem(strict_implies(X0,X1))) => is_a_theorem(X1))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_strict_implies)). 45.33/45.19 fof(f139,plain,( 45.33/45.19 modus_ponens_strict_implies), 45.33/45.19 inference(cnf_transformation,[],[f70])). 45.33/45.19 fof(f70,axiom,( 45.33/45.19 modus_ponens_strict_implies), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies)). 45.33/45.19 fof(f3164,plain,( 45.33/45.19 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(X2,implies(X3,X4))) | ~is_a_theorem(strict_implies(X2,equiv(X3,X4)))) )), 45.33/45.19 inference(resolution,[],[f853,f278])). 45.33/45.19 fof(f853,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (~is_a_theorem(strict_implies(X2,X1)) | ~is_a_theorem(strict_implies(X0,X2)) | is_a_theorem(strict_implies(X0,X1))) )), 45.33/45.19 inference(resolution,[],[f335,f177])). 45.33/45.19 fof(f335,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (~is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2))) | is_a_theorem(strict_implies(X0,X2))) )), 45.33/45.19 inference(resolution,[],[f179,f178])). 45.33/45.19 fof(f179,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))) )), 45.33/45.19 inference(global_subsumption,[],[f135,f162])). 45.33/45.19 fof(f162,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) | ~axiom_m5) )), 45.33/45.19 inference(cnf_transformation,[],[f126])). 45.33/45.19 fof(f126,plain,( 45.33/45.19 ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) | ~axiom_m5), 45.33/45.19 inference(ennf_transformation,[],[f100])). 45.33/45.19 fof(f100,plain,( 45.33/45.19 axiom_m5 => ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f91])). 45.33/45.19 fof(f91,plain,( 45.33/45.19 axiom_m5 <=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))), 45.33/45.19 inference(rectify,[],[f52])). 45.33/45.19 fof(f52,axiom,( 45.33/45.19 axiom_m5 <=> ! [X0,X1,X4] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X4)),strict_implies(X0,X4)))), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m5)). 45.33/45.19 fof(f135,plain,( 45.33/45.19 axiom_m5), 45.33/45.19 inference(cnf_transformation,[],[f61])). 45.33/45.19 fof(f61,axiom,( 45.33/45.19 axiom_m5), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m5)). 45.33/45.19 fof(f178100,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(X0,equiv(X1,X1)))) )), 45.33/45.19 inference(resolution,[],[f178099,f134690])). 45.33/45.19 fof(f134690,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(necessarily(not(not(X0)))) | is_a_theorem(strict_implies(X1,X0))) )), 45.33/45.19 inference(forward_demodulation,[],[f134665,f1708])). 45.33/45.19 fof(f1708,plain,( 45.33/45.19 ( ! [X0,X1] : (strict_implies(X1,X0) = strict_implies(and(not(X0),X1),X0)) )), 45.33/45.19 inference(forward_demodulation,[],[f1691,f168])). 45.33/45.19 fof(f1691,plain,( 45.33/45.19 ( ! [X0,X1] : (necessarily(implies(X1,X0)) = strict_implies(and(not(X0),X1),X0)) )), 45.33/45.19 inference(superposition,[],[f168,f1538])). 45.33/45.19 fof(f1538,plain,( 45.33/45.19 ( ! [X61,X62] : (implies(X62,X61) = implies(and(not(X61),X62),X61)) )), 45.33/45.19 inference(forward_demodulation,[],[f1500,f458])). 45.33/45.19 fof(f458,plain,( 45.33/45.19 ( ! [X28,X29] : (implies(X28,X29) = not(and(not(X29),X28))) )), 45.33/45.19 inference(superposition,[],[f169,f417])). 45.33/45.19 fof(f1500,plain,( 45.33/45.19 ( ! [X61,X62] : (implies(and(not(X61),X62),X61) = not(and(not(X61),X62))) )), 45.33/45.19 inference(superposition,[],[f169,f1430])). 45.33/45.19 fof(f1430,plain,( 45.33/45.19 ( ! [X2,X3] : (and(X2,X3) = and(and(X2,X3),X2)) )), 45.33/45.19 inference(resolution,[],[f1290,f500])). 45.33/45.19 fof(f500,plain,( 45.33/45.19 ( ! [X4,X5] : (is_a_theorem(strict_implies(and(X4,X5),and(X4,and(X4,X5))))) )), 45.33/45.19 inference(superposition,[],[f183,f479])). 45.33/45.19 fof(f183,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))) )), 45.33/45.19 inference(global_subsumption,[],[f138,f166])). 45.33/45.19 fof(f166,plain,( 45.33/45.19 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) | ~axiom_m3) )), 45.33/45.19 inference(cnf_transformation,[],[f130])). 45.33/45.19 fof(f130,plain,( 45.33/45.19 ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) | ~axiom_m3), 45.33/45.19 inference(ennf_transformation,[],[f101])). 45.33/45.19 fof(f101,plain,( 45.33/45.19 axiom_m3 => ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))), 45.33/45.19 inference(unused_predicate_definition_removal,[],[f98])). 45.33/45.19 fof(f98,plain,( 45.33/45.19 ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) <=> axiom_m3), 45.33/45.19 inference(rectify,[],[f51])). 45.33/45.19 fof(f51,axiom,( 45.33/45.19 ! [X0,X1,X4] : is_a_theorem(strict_implies(and(and(X0,X1),X4),and(X0,and(X1,X4)))) <=> axiom_m3), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m3)). 45.33/45.19 fof(f138,plain,( 45.33/45.19 axiom_m3), 45.33/45.19 inference(cnf_transformation,[],[f68])). 45.33/45.19 fof(f68,axiom,( 45.33/45.19 axiom_m3), 45.33/45.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m3)). 45.33/45.19 fof(f1290,plain,( 45.33/45.19 ( ! [X4,X5] : (~is_a_theorem(strict_implies(X4,and(X5,X4))) | and(X4,X5) = X4) )), 45.33/45.19 inference(superposition,[],[f404,f417])). 45.33/45.19 fof(f404,plain,( 45.33/45.19 ( ! [X10,X9] : (~is_a_theorem(strict_implies(X9,and(X9,X10))) | and(X9,X10) = X9) )), 45.33/45.19 inference(resolution,[],[f390,f174])). 45.33/45.19 fof(f134665,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(necessarily(not(not(X0)))) | is_a_theorem(strict_implies(and(not(X0),X1),X0))) )), 45.33/45.19 inference(superposition,[],[f134420,f617])). 45.33/45.19 fof(f617,plain,( 45.33/45.19 ( ! [X0] : (or(X0,X0) = not(not(X0))) )), 45.33/45.19 inference(superposition,[],[f507,f172])). 45.33/45.19 fof(f507,plain,( 45.33/45.19 ( ! [X17] : (implies(not(X17),X17) = not(not(X17))) )), 45.33/45.19 inference(superposition,[],[f169,f479])). 45.33/45.19 fof(f134420,plain,( 45.33/45.19 ( ! [X24,X23,X22] : (~is_a_theorem(necessarily(or(X22,X23))) | is_a_theorem(strict_implies(and(not(X22),X24),X23))) )), 45.33/45.19 inference(resolution,[],[f3199,f174])). 45.33/45.19 fof(f3199,plain,( 45.33/45.19 ( ! [X4,X5,X3] : (~is_a_theorem(strict_implies(X5,not(X3))) | ~is_a_theorem(necessarily(or(X3,X4))) | is_a_theorem(strict_implies(X5,X4))) )), 45.33/45.19 inference(superposition,[],[f853,f186])). 45.33/45.19 fof(f178099,plain,( 45.33/45.19 ( ! [X0] : (is_a_theorem(necessarily(not(not(equiv(X0,X0)))))) )), 45.33/45.19 inference(forward_demodulation,[],[f178075,f437])). 45.33/45.19 fof(f178075,plain,( 45.33/45.19 ( ! [X0] : (is_a_theorem(necessarily(not(not(implies(X0,X0)))))) )), 45.33/45.19 inference(superposition,[],[f175093,f617])). 45.33/45.19 fof(f175093,plain,( 45.33/45.19 ( ! [X881,X882,X880] : (is_a_theorem(necessarily(or(implies(X880,X881),implies(X882,X880))))) )), 45.33/45.19 inference(forward_demodulation,[],[f174205,f169])). 45.33/45.19 fof(f174205,plain,( 45.33/45.19 ( ! [X881,X882,X880] : (is_a_theorem(necessarily(or(implies(X880,X881),not(and(X882,not(X880))))))) )), 45.33/45.19 inference(superposition,[],[f28347,f173234])). 45.33/45.19 fof(f173234,plain,( 45.33/45.19 ( ! [X6,X5] : (and(implies(X5,X6),not(X5)) = not(X5)) )), 45.33/45.19 inference(resolution,[],[f172704,f1833])). 45.33/45.19 fof(f1833,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(strict_implies(implies(X1,X0),X0)) | and(X1,not(X0)) = not(X0)) )), 45.33/45.19 inference(forward_demodulation,[],[f1832,f168])). 45.33/45.19 fof(f1832,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(necessarily(implies(implies(X1,X0),X0))) | and(X1,not(X0)) = not(X0)) )), 45.33/45.19 inference(forward_demodulation,[],[f1831,f744])). 45.33/45.19 fof(f744,plain,( 45.33/45.19 ( ! [X4,X2,X3] : (implies(implies(X2,X3),X4) = or(X4,and(X2,not(X3)))) )), 45.33/45.19 inference(superposition,[],[f718,f169])). 45.33/45.19 fof(f718,plain,( 45.33/45.19 ( ! [X2,X3] : (implies(not(X2),X3) = or(X3,X2)) )), 45.33/45.19 inference(forward_demodulation,[],[f696,f172])). 45.33/45.19 fof(f696,plain,( 45.33/45.19 ( ! [X2,X3] : (implies(not(X2),X3) = implies(not(X3),X2)) )), 45.33/45.19 inference(superposition,[],[f458,f169])). 45.33/45.19 fof(f1831,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(necessarily(or(X0,and(X1,not(X0))))) | and(X1,not(X0)) = not(X0)) )), 45.33/45.19 inference(forward_demodulation,[],[f1823,f821])). 45.33/45.19 fof(f821,plain,( 45.33/45.19 ( ! [X2,X3] : (necessarily(or(X2,X3)) = necessarily(or(X3,X2))) )), 45.33/45.19 inference(superposition,[],[f752,f186])). 45.33/45.19 fof(f752,plain,( 45.33/45.19 ( ! [X4,X3] : (necessarily(or(X4,X3)) = strict_implies(not(X3),X4)) )), 45.33/45.19 inference(superposition,[],[f168,f718])). 45.33/45.19 fof(f1823,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(necessarily(or(and(X1,not(X0)),X0))) | and(X1,not(X0)) = not(X0)) )), 45.33/45.19 inference(superposition,[],[f534,f752])). 45.33/45.19 fof(f534,plain,( 45.33/45.19 ( ! [X0,X1] : (~is_a_theorem(strict_implies(X0,and(X1,X0))) | and(X1,X0) = X0) )), 45.33/45.19 inference(resolution,[],[f447,f390])). 45.33/45.19 fof(f172704,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(implies(implies(X0,X1),X0),X0))) )), 45.33/45.19 inference(superposition,[],[f172516,f744])). 45.33/45.19 fof(f172516,plain,( 45.33/45.19 ( ! [X0,X1] : (is_a_theorem(strict_implies(or(X0,and(X0,X1)),X0))) )), 45.33/45.19 inference(superposition,[],[f169423,f1708])). 45.33/45.19 fof(f169423,plain,( 45.33/45.19 ( ! [X47,X45,X46] : (is_a_theorem(strict_implies(and(not(X45),or(X45,and(X46,X47))),X46))) )), 45.33/45.19 inference(resolution,[],[f168995,f3179])). 45.33/45.19 fof(f3179,plain,( 45.33/45.19 ( ! [X45,X43,X44] : (~is_a_theorem(strict_implies(X43,and(X44,X45))) | is_a_theorem(strict_implies(X43,X44))) )), 45.33/45.19 inference(resolution,[],[f853,f174])). 45.33/45.19 fof(f168995,plain,( 45.33/45.19 ( ! [X26,X27] : (is_a_theorem(strict_implies(and(not(X27),or(X27,X26)),X26))) )), 45.33/45.19 inference(forward_demodulation,[],[f168994,f54954])). 45.33/45.19 fof(f54954,plain,( 45.33/45.19 ( ! [X4,X5,X3] : (strict_implies(and(X3,X4),X5) = strict_implies(and(X4,X3),X5)) )), 45.33/45.19 inference(superposition,[],[f48895,f168])). 45.33/45.19 fof(f48895,plain,( 45.33/45.19 ( ! [X130,X131,X129] : (necessarily(implies(and(X130,X129),X131)) = strict_implies(and(X129,X130),X131)) )), 45.33/45.19 inference(superposition,[],[f168,f48631])). 45.33/45.19 fof(f48631,plain,( 45.33/45.19 ( ! [X14,X15,X13] : (implies(and(X13,X14),X15) = implies(and(X14,X13),X15)) )), 45.33/45.19 inference(global_subsumption,[],[f29531,f48477])). 45.33/45.19 fof(f48477,plain,( 45.33/45.19 ( ! [X14,X15,X13] : (~is_a_theorem(strict_implies(implies(and(X13,X14),X15),implies(and(X14,X13),X15))) | implies(and(X13,X14),X15) = implies(and(X14,X13),X15)) )), 45.33/45.19 inference(resolution,[],[f29531,f390])). 45.33/45.19 fof(f29531,plain,( 45.33/45.19 ( ! [X165,X163,X164] : (is_a_theorem(strict_implies(implies(and(X163,X164),X165),implies(and(X164,X163),X165)))) )), 45.33/45.19 inference(superposition,[],[f28351,f10066])). 45.33/45.19 fof(f10066,plain,( 45.33/45.19 ( ! [X111,X112] : (and(X111,X112) = and(and(X112,X111),and(X111,X112))) )), 45.33/45.19 inference(superposition,[],[f1548,f9757])). 45.33/45.19 fof(f9757,plain,( 45.33/45.19 ( ! [X6,X7] : (and(X6,X7) = and(X6,and(X7,X6))) )), 45.33/45.19 inference(superposition,[],[f9334,f479])). 45.33/45.19 fof(f9334,plain,( 45.33/45.19 ( ! [X12,X10,X11] : (and(X11,and(X10,X12)) = and(and(X11,X12),X10)) )), 45.33/45.19 inference(superposition,[],[f9013,f417])). 45.33/45.20 fof(f9013,plain,( 45.33/45.20 ( ! [X17,X18,X16] : (and(X16,and(X17,X18)) = and(X17,and(X16,X18))) )), 45.33/45.20 inference(global_subsumption,[],[f7113,f9012])). 45.33/45.20 fof(f9012,plain,( 45.33/45.20 ( ! [X17,X18,X16] : (and(X16,and(X17,X18)) = and(X17,and(X16,X18)) | ~is_a_theorem(strict_implies(and(X16,and(X17,X18)),and(X17,and(X16,X18))))) )), 45.33/45.20 inference(forward_demodulation,[],[f8780,f8777])). 45.33/45.20 fof(f8777,plain,( 45.33/45.20 ( ! [X17,X18,X16] : (and(X16,and(X17,X18)) = and(and(X17,X16),X18)) )), 45.33/45.20 inference(subsumption_resolution,[],[f7014,f8725])). 45.33/45.20 fof(f8725,plain,( 45.33/45.20 ( ! [X6,X4,X5] : (is_a_theorem(strict_implies(and(X6,and(X4,X5)),and(and(X4,X6),X5)))) )), 45.33/45.20 inference(superposition,[],[f7009,f417])). 45.33/45.20 fof(f7009,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (is_a_theorem(strict_implies(and(and(X0,X1),X2),and(and(X0,X2),X1)))) )), 45.33/45.20 inference(resolution,[],[f451,f3180])). 45.33/45.20 fof(f3180,plain,( 45.33/45.20 ( ! [X47,X48,X46] : (~is_a_theorem(strict_implies(X46,and(X47,X48))) | is_a_theorem(strict_implies(X46,and(X48,X47)))) )), 45.33/45.20 inference(resolution,[],[f853,f175])). 45.33/45.20 fof(f451,plain,( 45.33/45.20 ( ! [X12,X10,X11] : (is_a_theorem(strict_implies(and(and(X11,X10),X12),and(X10,and(X11,X12))))) )), 45.33/45.20 inference(superposition,[],[f183,f417])). 45.33/45.20 fof(f7014,plain,( 45.33/45.20 ( ! [X17,X18,X16] : (~is_a_theorem(strict_implies(and(X16,and(X17,X18)),and(and(X17,X16),X18))) | and(X16,and(X17,X18)) = and(and(X17,X16),X18)) )), 45.33/45.20 inference(resolution,[],[f451,f390])). 45.33/45.20 fof(f8780,plain,( 45.33/45.20 ( ! [X17,X18,X16] : (~is_a_theorem(strict_implies(and(X16,and(X17,X18)),and(X17,and(X16,X18)))) | and(X16,and(X17,X18)) = and(and(X16,X17),X18)) )), 45.33/45.20 inference(backward_demodulation,[],[f8777,f407])). 45.33/45.20 fof(f407,plain,( 45.33/45.20 ( ! [X17,X18,X16] : (~is_a_theorem(strict_implies(and(X16,and(X17,X18)),and(and(X16,X17),X18))) | and(X16,and(X17,X18)) = and(and(X16,X17),X18)) )), 45.33/45.20 inference(resolution,[],[f390,f183])). 45.33/45.20 fof(f7113,plain,( 45.33/45.20 ( ! [X6,X4,X5] : (is_a_theorem(strict_implies(and(X6,and(X4,X5)),and(X4,and(X6,X5))))) )), 45.33/45.20 inference(superposition,[],[f452,f417])). 45.33/45.20 fof(f452,plain,( 45.33/45.20 ( ! [X14,X15,X13] : (is_a_theorem(strict_implies(and(and(X15,X13),X14),and(X15,and(X14,X13))))) )), 45.33/45.20 inference(superposition,[],[f183,f417])). 45.33/45.20 fof(f1548,plain,( 45.33/45.20 ( ! [X4,X3] : (and(X3,X4) = and(X4,and(X3,X4))) )), 45.33/45.20 inference(superposition,[],[f1429,f417])). 45.33/45.20 fof(f1429,plain,( 45.33/45.20 ( ! [X0,X1] : (and(X0,X1) = and(and(X0,X1),X1)) )), 45.33/45.20 inference(resolution,[],[f1290,f998])). 45.33/45.20 fof(f998,plain,( 45.33/45.20 ( ! [X4,X5] : (is_a_theorem(strict_implies(and(X5,X4),and(X4,and(X5,X4))))) )), 45.33/45.20 inference(superposition,[],[f500,f417])). 45.33/45.20 fof(f28351,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(implies(X2,X3),implies(and(X2,X4),X3)))) )), 45.33/45.20 inference(forward_demodulation,[],[f28350,f458])). 45.33/45.20 fof(f28350,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(implies(X2,X3),not(and(not(X3),and(X2,X4)))))) )), 45.33/45.20 inference(forward_demodulation,[],[f28349,f8777])). 45.33/45.20 fof(f28349,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (is_a_theorem(strict_implies(implies(X2,X3),not(and(and(X2,not(X3)),X4))))) )), 45.33/45.20 inference(forward_demodulation,[],[f28344,f168])). 45.33/45.20 fof(f28344,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (is_a_theorem(necessarily(implies(implies(X2,X3),not(and(and(X2,not(X3)),X4)))))) )), 45.33/45.20 inference(superposition,[],[f28228,f196])). 45.33/45.20 fof(f196,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (implies(implies(X0,X1),X2) = or(and(X0,not(X1)),X2)) )), 45.33/45.20 inference(superposition,[],[f172,f169])). 45.33/45.20 fof(f28228,plain,( 45.33/45.20 ( ! [X4,X5] : (is_a_theorem(necessarily(or(X4,not(and(X4,X5)))))) )), 45.33/45.20 inference(forward_demodulation,[],[f28127,f821])). 45.33/45.20 fof(f28127,plain,( 45.33/45.20 ( ! [X4,X5] : (is_a_theorem(necessarily(or(not(and(X4,X5)),X4)))) )), 45.33/45.20 inference(resolution,[],[f3234,f482])). 45.33/45.20 fof(f3234,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (~is_a_theorem(necessarily(or(and(X1,X2),X0))) | is_a_theorem(necessarily(or(X0,X1)))) )), 45.33/45.20 inference(forward_demodulation,[],[f3229,f186])). 45.33/45.20 fof(f3229,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (~is_a_theorem(necessarily(or(and(X1,X2),X0))) | is_a_theorem(strict_implies(not(X0),X1))) )), 45.33/45.20 inference(superposition,[],[f3179,f752])). 45.33/45.20 fof(f168994,plain,( 45.33/45.20 ( ! [X26,X27] : (is_a_theorem(strict_implies(and(or(X27,X26),not(X27)),X26))) )), 45.33/45.20 inference(forward_demodulation,[],[f168993,f168])). 45.33/45.20 fof(f168993,plain,( 45.33/45.20 ( ! [X26,X27] : (is_a_theorem(necessarily(implies(and(or(X27,X26),not(X27)),X26)))) )), 45.33/45.20 inference(forward_demodulation,[],[f168992,f9474])). 45.33/45.20 fof(f9474,plain,( 45.33/45.20 ( ! [X385,X384,X386] : (implies(and(X385,X386),X384) = not(and(X385,and(not(X384),X386)))) )), 45.33/45.20 inference(superposition,[],[f458,f9013])). 45.33/45.20 fof(f168992,plain,( 45.33/45.20 ( ! [X26,X27] : (is_a_theorem(necessarily(not(and(or(X27,X26),and(not(X26),not(X27))))))) )), 45.33/45.20 inference(forward_demodulation,[],[f168709,f168934])). 45.33/45.20 fof(f168934,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(X23,or(X22,X21)))) = necessarily(not(and(or(X21,X22),X23)))) )), 45.33/45.20 inference(forward_demodulation,[],[f168933,f89578])). 45.33/45.20 fof(f89578,plain,( 45.33/45.20 ( ! [X43,X44,X42] : (not(and(or(X42,X43),X44)) = not(and(or(X43,X42),and(X44,or(X42,X43))))) )), 45.33/45.20 inference(superposition,[],[f62068,f9757])). 45.33/45.20 fof(f62068,plain,( 45.33/45.20 ( ! [X4,X5,X3] : (not(and(or(X4,X5),X3)) = not(and(or(X5,X4),X3))) )), 45.33/45.20 inference(forward_demodulation,[],[f62067,f172])). 45.33/45.20 fof(f62067,plain,( 45.33/45.20 ( ! [X4,X5,X3] : (not(and(or(X5,X4),X3)) = not(and(implies(not(X4),X5),X3))) )), 45.33/45.20 inference(forward_demodulation,[],[f61791,f172])). 45.33/45.20 fof(f61791,plain,( 45.33/45.20 ( ! [X4,X5,X3] : (not(and(implies(not(X4),X5),X3)) = not(and(implies(not(X5),X4),X3))) )), 45.33/45.20 inference(superposition,[],[f692,f691])). 45.33/45.20 fof(f691,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (implies(X4,and(X2,not(X3))) = not(and(implies(X2,X3),X4))) )), 45.33/45.20 inference(superposition,[],[f458,f169])). 45.33/45.20 fof(f692,plain,( 45.33/45.20 ( ! [X6,X7,X5] : (implies(X7,and(not(X5),X6)) = not(and(implies(X6,X5),X7))) )), 45.33/45.20 inference(superposition,[],[f458,f458])). 45.33/45.20 fof(f168933,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(X23,or(X22,X21)))) = necessarily(not(and(or(X22,X21),and(X23,or(X21,X22)))))) )), 45.33/45.20 inference(forward_demodulation,[],[f168932,f172])). 45.33/45.20 fof(f168932,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(X23,or(X22,X21)))) = necessarily(not(and(or(X22,X21),and(X23,implies(not(X21),X22)))))) )), 45.33/45.20 inference(forward_demodulation,[],[f168931,f49141])). 45.33/45.20 fof(f49141,plain,( 45.33/45.20 ( ! [X21,X19,X20,X18] : (implies(and(X19,X18),and(X20,not(X21))) = not(and(X19,and(X18,implies(X20,X21))))) )), 45.33/45.20 inference(forward_demodulation,[],[f48798,f8777])). 45.33/45.20 fof(f48798,plain,( 45.33/45.20 ( ! [X21,X19,X20,X18] : (implies(and(X19,X18),and(X20,not(X21))) = not(and(and(X18,X19),implies(X20,X21)))) )), 45.33/45.20 inference(superposition,[],[f48631,f195])). 45.33/45.20 fof(f195,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (implies(X4,and(X2,not(X3))) = not(and(X4,implies(X2,X3)))) )), 45.33/45.20 inference(superposition,[],[f169,f169])). 45.33/45.20 fof(f168931,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(X23,or(X22,X21)))) = necessarily(implies(and(or(X22,X21),X23),and(not(X21),not(X22))))) )), 45.33/45.20 inference(forward_demodulation,[],[f168930,f9474])). 45.33/45.20 fof(f168930,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(X23,or(X22,X21)))) = necessarily(not(and(or(X22,X21),and(not(and(not(X21),not(X22))),X23))))) )), 45.33/45.20 inference(forward_demodulation,[],[f168929,f62070])). 45.33/45.20 fof(f62070,plain,( 45.33/45.20 ( ! [X6,X8,X7] : (not(and(X6,or(X7,X8))) = not(and(or(X8,X7),X6))) )), 45.33/45.20 inference(forward_demodulation,[],[f62069,f172])). 45.33/45.20 fof(f62069,plain,( 45.33/45.20 ( ! [X6,X8,X7] : (not(and(or(X8,X7),X6)) = not(and(X6,implies(not(X7),X8)))) )), 45.33/45.20 inference(forward_demodulation,[],[f61792,f172])). 45.33/45.20 fof(f61792,plain,( 45.33/45.20 ( ! [X6,X8,X7] : (not(and(X6,implies(not(X7),X8))) = not(and(implies(not(X8),X7),X6))) )), 45.33/45.20 inference(superposition,[],[f692,f195])). 45.33/45.20 fof(f168929,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(X23,or(X22,X21)))) = necessarily(not(and(and(not(and(not(X21),not(X22))),X23),or(X21,X22))))) )), 45.33/45.20 inference(forward_demodulation,[],[f168686,f38824])). 45.33/45.20 fof(f38824,plain,( 45.33/45.20 ( ! [X28,X26,X27] : (necessarily(not(and(X28,or(X27,X26)))) = strict_implies(X28,and(not(X26),not(X27)))) )), 45.33/45.20 inference(superposition,[],[f2746,f718])). 45.33/45.20 fof(f2746,plain,( 45.33/45.20 ( ! [X4,X2,X3] : (necessarily(not(and(X2,implies(X3,X4)))) = strict_implies(X2,and(X3,not(X4)))) )), 45.33/45.20 inference(superposition,[],[f168,f195])). 45.33/45.20 fof(f168686,plain,( 45.33/45.20 ( ! [X23,X21,X22] : (necessarily(not(and(and(not(and(not(X21),not(X22))),X23),or(X21,X22)))) = strict_implies(X23,and(not(X21),not(X22)))) )), 45.33/45.20 inference(superposition,[],[f38825,f1708])). 45.33/45.20 fof(f38825,plain,( 45.33/45.20 ( ! [X30,X31,X29] : (necessarily(not(and(X31,or(X29,X30)))) = strict_implies(X31,and(not(X29),not(X30)))) )), 45.33/45.20 inference(superposition,[],[f2746,f172])). 45.33/45.20 fof(f168709,plain,( 45.33/45.20 ( ! [X26,X27] : (is_a_theorem(necessarily(not(and(and(not(X26),not(X27)),or(X26,X27)))))) )), 45.33/45.20 inference(superposition,[],[f481,f38825])). 45.33/45.20 fof(f481,plain,( 45.33/45.20 ( ! [X0] : (is_a_theorem(strict_implies(X0,X0))) )), 45.33/45.20 inference(backward_demodulation,[],[f479,f180])). 45.33/45.20 fof(f28347,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (is_a_theorem(necessarily(or(X0,not(and(X1,and(X0,X2))))))) )), 45.33/45.20 inference(forward_demodulation,[],[f28346,f8777])). 45.33/45.20 fof(f28346,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (is_a_theorem(necessarily(or(X0,not(and(and(X0,X1),X2)))))) )), 45.33/45.20 inference(forward_demodulation,[],[f28270,f821])). 45.33/45.20 fof(f28270,plain,( 45.33/45.20 ( ! [X2,X0,X1] : (is_a_theorem(necessarily(or(not(and(and(X0,X1),X2)),X0)))) )), 45.33/45.20 inference(resolution,[],[f28228,f3234])). 45.33/45.20 fof(f178137,plain,( 45.33/45.20 ~is_a_theorem(equiv(sK0,sK0))), 45.33/45.20 inference(backward_demodulation,[],[f178112,f181])). 45.33/45.20 fof(f181,plain,( 45.33/45.20 ~is_a_theorem(implies(and(sK0,sK1),sK0))), 45.33/45.20 inference(global_subsumption,[],[f133,f164])). 45.33/45.20 fof(f164,plain,( 45.33/45.20 and_1 | ~is_a_theorem(implies(and(sK0,sK1),sK0))), 45.33/45.20 inference(cnf_transformation,[],[f132])). 45.33/45.20 fof(f132,plain,( 45.33/45.20 and_1 | ~is_a_theorem(implies(and(sK0,sK1),sK0))), 45.33/45.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f128,f131])). 45.33/45.20 fof(f131,plain,( 45.33/45.20 ? [X0,X1] : ~is_a_theorem(implies(and(X0,X1),X0)) => ~is_a_theorem(implies(and(sK0,sK1),sK0))), 45.33/45.20 introduced(choice_axiom,[])). 45.33/45.20 fof(f128,plain,( 45.33/45.20 and_1 | ? [X0,X1] : ~is_a_theorem(implies(and(X0,X1),X0))), 45.33/45.20 inference(ennf_transformation,[],[f107])). 45.33/45.20 fof(f107,plain,( 45.33/45.20 ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) => and_1), 45.33/45.20 inference(unused_predicate_definition_removal,[],[f21])). 45.33/45.20 fof(f21,axiom,( 45.33/45.20 ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) <=> and_1), 45.33/45.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1)). 45.33/45.20 fof(f133,plain,( 45.33/45.20 ~and_1), 45.33/45.20 inference(cnf_transformation,[],[f79])). 45.33/45.20 fof(f79,plain,( 45.33/45.20 ~and_1), 45.33/45.20 inference(flattening,[],[f76])). 45.33/45.20 fof(f76,negated_conjecture,( 45.33/45.20 ~and_1), 45.33/45.20 inference(negated_conjecture,[],[f75])). 45.33/45.20 fof(f75,conjecture,( 45.33/45.20 and_1), 45.33/45.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1)). 45.33/45.20 fof(f178112,plain,( 45.33/45.20 ( ! [X8,X7] : (equiv(X7,X7) = implies(and(X7,X8),X7)) )), 45.33/45.20 inference(subsumption_resolution,[],[f29839,f178100])). 45.33/45.20 fof(f29839,plain,( 45.33/45.20 ( ! [X8,X7] : (~is_a_theorem(strict_implies(implies(and(X7,X8),X7),equiv(X7,X7))) | equiv(X7,X7) = implies(and(X7,X8),X7)) )), 45.33/45.20 inference(resolution,[],[f29474,f390])). 45.33/45.20 fof(f29474,plain,( 45.33/45.20 ( ! [X6,X7] : (is_a_theorem(strict_implies(equiv(X6,X6),implies(and(X6,X7),X6)))) )), 45.33/45.20 inference(superposition,[],[f28351,f437])). 45.33/45.20 % SZS output end Proof for theBenchmark 45.33/45.20 % ------------------------------ 45.33/45.20 % Version: Vampire 4.4.0 (commit 7916d27 on 2019-08-23 08:50:16 +0100) 45.33/45.20 % Termination reason: Refutation 45.33/45.20 45.33/45.20 % Memory used [KB]: 187033 45.33/45.20 % Time elapsed: 6.370 s 45.33/45.20 % ------------------------------ 45.33/45.20 % ------------------------------ 45.42/45.21 % Success in time 44.853 s 45.42/45.21 EOF