0.00/0.03	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.05	% Command  : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.09/0.42	% Computer : n007.cluster.edu
0.09/0.42	% Model    : x86_64 x86_64
0.09/0.42	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.09/0.42	% Memory   : 8046.5625MB
0.09/0.42	% OS       : Linux 6.8.0-71-generic
0.09/0.42	% CPULimit : 1440
0.09/0.42	% WCLimit  : 180
0.09/0.42	% DateTime : Mon Jul 27 08:57:04 UTC 2026
0.09/0.43	% CPUTime  : 
0.09/0.43	Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.13/0.46	Running higher-order theorem proving
0.13/0.47	Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 180 /export/starexec/sandbox/benchmark/theBenchmark.p
0.13/0.52	% (874437)Detected a higher-order problem, will run a greedy HOL sequence.
0.13/0.52	% (874446)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3619765859:i=24:av=off:rtra=on_1799 on theBenchmark for (1799ds/24Mi)
0.13/0.52	% (874446)Refutation not found, incomplete strategy
0.13/0.52	% (874446)------------------------------
0.13/0.52	% (874446)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.13/0.52	% (874446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.13/0.52	% (874446)CaDiCaL version: 2.1.3
0.13/0.52	% (874446)Termination reason: Refutation not found, incomplete strategy
0.13/0.52	% (874446)Time elapsed: 0.001 s
0.13/0.52	% (874446)Peak memory usage: 11 MB
0.13/0.52	% (874446)Instructions burned: 3 (million)
0.13/0.52	% (874446)------------------------------
0.13/0.52	% (874446)------------------------------
0.13/0.52	% (874448)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
0.13/0.52	% (874448)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
0.13/0.52	% (874442)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2278128144:s2a=on:i=87:rtra=on:ntd=on_1799 on theBenchmark for (1799ds/87Mi)
0.13/0.52	% (874443)lrs+10_16_si=on:nwc=1.5:random_seed=28596282:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_1799 on theBenchmark for (1799ds/18Mi)
0.13/0.52	% (874444)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4184402933:i=3:rtra=on:inj=on:ntd=on_1799 on theBenchmark for (1799ds/3Mi)
0.13/0.52	% (874448)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2063759348:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_1799 on theBenchmark for (1799ds/157Mi)
0.13/0.52	% (874445)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1274454740:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_1799 on theBenchmark for (1799ds/634Mi)
0.13/0.52	% (874447)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3549743301:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_1799 on theBenchmark for (1799ds/75Mi)
0.13/0.52	% (874444)Instruction limit reached! 
0.13/0.52	% (874444)------------------------------
0.13/0.52	% (874444)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.13/0.52	% (874444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.13/0.52	% (874444)CaDiCaL version: 2.1.3
0.13/0.52	% (874444)Termination reason: Instruction limit
0.13/0.52	% (874444)Termination phase: Saturation
0.13/0.52	% (874444)Time elapsed: 0.002 s
0.13/0.52	% (874444)Peak memory usage: 12 MB
0.13/0.52	% (874444)Instructions burned: 3 (million)
0.13/0.52	% (874442)Refutation not found, incomplete strategy
0.13/0.52	% (874442)------------------------------
0.13/0.52	% (874442)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.13/0.52	% (874442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.13/0.52	% (874442)CaDiCaL version: 2.1.3
0.13/0.52	% (874442)Termination reason: Refutation not found, incomplete strategy
0.13/0.52	% (874442)Time elapsed: 0.002 s
0.13/0.52	% (874442)Peak memory usage: 12 MB
0.13/0.52	% (874442)Instructions burned: 3 (million)
0.13/0.52	% (874442)------------------------------
0.13/0.52	% (874442)------------------------------
0.13/0.52	% (874450)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3286324575:i=2:hud=10:rtra=on_1799 on theBenchmark for (1799ds/2Mi)
0.13/0.52	% (874450)Instruction limit reached! 
0.13/0.52	% (874450)------------------------------
0.13/0.52	% (874450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.13/0.52	% (874450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.13/0.52	% (874450)CaDiCaL version: 2.1.3
0.13/0.52	% (874450)Termination reason: Instruction limit
0.13/0.52	% (874450)Termination phase: Saturation
0.13/0.52	% (874450)Time elapsed: 0.001 s
0.13/0.52	% (874450)Peak memory usage: 12 MB
0.13/0.52	% (874450)Instructions burned: 2 (million)
0.13/0.52	% (874445) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-874437-874445"...
0.13/0.52	% (874443)Instruction limit reached! 
0.13/0.52	% (874443)------------------------------
0.13/0.52	% (874443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.13/0.52	% (874443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.13/0.52	% (874443)CaDiCaL version: 2.1.3
0.13/0.52	% (874443)Termination reason: Instruction limit
0.13/0.52	% (874443)Termination phase: Saturation
0.13/0.52	% (874443)Time elapsed: 0.009 s
0.13/0.52	% (874443)Peak memory usage: 12 MB
0.13/0.52	% (874443)Instructions burned: 19 (million)
0.13/0.52	% (874445)...printing done.
0.13/0.52	% (874445)Refutation found. Thanks to Tanya!
0.13/0.52	% SZS status Theorem for theBenchmark
0.13/0.52	% SZS output start Proof for theBenchmark
0.13/0.52	thf(type_def_5, type, num: $tType).
0.13/0.52	thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
0.13/0.52	thf(func_def_0, type, holdsDuring_THFTYPE_IiooI: ($i > $o > $o)).
0.13/0.52	thf(func_def_7, type, lYearFn_THFTYPE_IiiI: ($i > $i)).
0.13/0.52	thf(func_def_8, type, likes_THFTYPE_IiioI: ($i > $i > $o)).
0.13/0.52	thf(func_def_10, type, parent_THFTYPE_IiioI: ($i > $i > $o)).
0.13/0.53	thf(func_def_12, type, vNOT: ($o > $o)).
0.13/0.53	thf(func_def_13, type, vAND: ($o > $o > $o)).
0.13/0.53	thf(func_def_14, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
0.13/0.53	thf(func_def_15, type, db1: !>[X0: $tType]:(X0)).
0.13/0.53	thf(func_def_16, type, db0: !>[X0: $tType]:(X0)).
0.13/0.53	thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
0.13/0.53	thf(func_def_21, type, sK1: (($i > $i > $o) > $i)).
0.13/0.53	thf(func_def_22, type, sK2: (($i > $i > $o) > $i)).
0.13/0.53	thf(func_def_23, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
0.13/0.53	thf(f2,conjecture,(
0.13/0.53	  ? [X0 : ($i > $i > $o)] : (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i) & (~ ! [X2 : $i,X1 : $i] : (X0 @ X1 @ X2)))),
0.13/0.53	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
0.13/0.53	thf(f3,negated_conjecture,(
0.13/0.53	  ~ ? [X0 : ($i > $i > $o)] : (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i) & (~ ! [X2 : $i,X1 : $i] : (X0 @ X1 @ X2)))),
0.13/0.53	  inference(negated_conjecture,[status(cth)],[f2])).
0.13/0.53	thf(f6,axiom,(
0.13/0.53	  (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))),
0.13/0.53	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_004)).
0.13/0.53	thf(f8,axiom,(
0.13/0.53	  (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)))),
0.13/0.53	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_007)).
0.13/0.53	thf(f9,axiom,(
0.13/0.53	  (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i))),
0.13/0.53	  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_002)).
0.13/0.53	thf(f11,plain,(
0.13/0.53	  ~ ? [X0 : ($i > $i > $o)] : (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i) & (~ ! [X1 : $i,X2 : $i] : (X0 @ X2 @ X1)))),
0.13/0.53	  inference(rectify,[],[f3])).
0.13/0.53	thf(f12,plain,(
0.13/0.53	  ~ ? [X0 : ($i > $i > $o)] : ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))))),
0.13/0.53	  inference(fool_elimination,[],[f11])).
0.13/0.53	thf(f13,plain,(
0.13/0.53	  (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))),
0.13/0.53	  inference(rectify,[],[f6])).
0.13/0.53	thf(f14,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))) = $true)),
0.13/0.53	  inference(fool_elimination,[],[f13])).
0.13/0.53	thf(f15,plain,(
0.13/0.53	  (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)))),
0.13/0.53	  inference(rectify,[],[f8])).
0.13/0.53	thf(f16,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)))) = $true)),
0.13/0.53	  inference(fool_elimination,[],[f15])).
0.13/0.53	thf(f21,plain,(
0.13/0.53	  (holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i))),
0.13/0.53	  inference(rectify,[],[f9])).
0.13/0.53	thf(f22,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i))) = $true)),
0.13/0.53	  inference(fool_elimination,[],[f21])).
0.13/0.53	thf(f29,plain,(
0.13/0.53	  ! [X0 : ($i > $i > $o)] : ($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))))),
0.13/0.53	  inference(ennf_transformation,[],[f12])).
0.13/0.53	thf(f31,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)))) = $true)),
0.13/0.53	  inference(cnf_transformation,[],[f16])).
0.13/0.53	thf(f32,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i))) = $true)),
0.13/0.53	  inference(cnf_transformation,[],[f22])).
0.13/0.53	thf(f37,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))) = $true)),
0.13/0.53	  inference(cnf_transformation,[],[f14])).
0.13/0.53	thf(f38,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (X0 @ Y0 @ Y1)))))) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))))) )),
0.13/0.53	  inference(cnf_transformation,[],[f29])).
0.13/0.53	thf(f40,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))))) )),
0.13/0.53	  inference(beta-eta_normalization,[],[f38])).
0.13/0.53	thf(f42,definition,(
0.13/0.53	  spl0_1 <=> (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i))) = $true)),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
0.13/0.53	thf(f44,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i))) = $true) | ~spl0_1),
0.13/0.53	  inference(avatar_component_clause,[],[f42])).
0.13/0.53	thf(f45,plain,(
0.13/0.53	  spl0_1),
0.13/0.53	  inference(avatar_split_clause,[],[f32,f42])).
0.13/0.53	thf(f67,definition,(
0.13/0.53	  spl0_6 <=> (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))) = $true)),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition])).
0.13/0.53	thf(f69,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))) = $true) | ~spl0_6),
0.13/0.53	  inference(avatar_component_clause,[],[f67])).
0.13/0.53	thf(f70,plain,(
0.13/0.53	  spl0_6),
0.13/0.53	  inference(avatar_split_clause,[],[f37,f67])).
0.13/0.53	thf(f77,definition,(
0.13/0.53	  spl0_8 <=> (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)))) = $true)),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition])).
0.13/0.53	thf(f79,plain,(
0.13/0.53	  (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ (likes_THFTYPE_IiioI @ lSue_THFTYPE_i @ lMary_THFTYPE_i)))) = $true) | ~spl0_8),
0.13/0.53	  inference(avatar_component_clause,[],[f77])).
0.13/0.53	thf(f80,plain,(
0.13/0.53	  spl0_8),
0.13/0.53	  inference(avatar_split_clause,[],[f31,f77])).
0.13/0.53	thf(f87,definition,(
0.13/0.53	  spl0_10 <=> (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) = $true)),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition])).
0.13/0.53	thf(f115,plain,(
0.13/0.53	  (((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) = $true) | ~spl0_6),
0.13/0.53	  inference(fool_paramodulation,[],[f69])).
0.13/0.53	thf(f117,definition,(
0.13/0.53	  spl0_15 <=> (((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false)),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition])).
0.13/0.53	thf(f120,plain,(
0.13/0.53	  spl0_15 | spl0_10 | ~spl0_6),
0.13/0.53	  inference(avatar_split_clause,[],[f115,f67,f87,f117])).
0.13/0.53	thf(f127,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ $true) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))) != $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) = $false)) )),
0.13/0.53	  inference(fool_paramodulation,[],[f40])).
0.13/0.53	thf(f132,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true) | (((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i))) = $false)) )),
0.13/0.53	  inference(fool_paramodulation,[],[f40])).
0.13/0.53	thf(f134,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true) | (((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))))) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i))) = $false)) )),
0.13/0.53	  inference(and_proxy_clausification,[],[f132])).
0.13/0.53	thf(f135,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0)))))) = $false) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true)) )),
0.13/0.53	  inference(and_proxy_clausification,[],[f134])).
0.13/0.53	thf(f136,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (X0 @ Y0)))))) | (((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true) | (((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false)) )),
0.13/0.53	  inference(not_proxy_clausification,[],[f135])).
0.13/0.53	thf(f137,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o),X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))) @ X1))) | (((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true) | (((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false)) )),
0.13/0.53	  inference(pi_proxy_clausification,[],[f136])).
0.13/0.53	thf(f138,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o),X1 : $i] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true) | (((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | ($true = ((!! @ $i @ (X0 @ X1))))) )),
0.13/0.53	  inference(beta-eta_normalization,[],[f137])).
0.13/0.53	thf(f139,plain,(
0.13/0.53	  ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : ((((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $true)) != $true) | (((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((X0 @ X1 @ X2)) = $true)) )),
0.13/0.53	  inference(pi_proxy_clausification,[],[f138])).
0.13/0.53	thf(f141,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ $true) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))) != $true) | ((((^[Y0 : $i]: (!! @ $i @ (X0 @ Y0))) @ (sK1 @ X0))) = $false)) )),
0.13/0.53	  inference(sigma_proxy_clausification,[],[f127])).
0.13/0.53	thf(f142,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ $true) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))) != $true) | (((!! @ $i @ (X0 @ (sK1 @ X0)))) = $false)) )),
0.13/0.53	  inference(beta-eta_normalization,[],[f141])).
0.13/0.53	thf(f143,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (((~ $true) & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))) != $true) | (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $false)) )),
0.13/0.53	  inference(sigma_proxy_clausification,[],[f142])).
0.13/0.53	thf(f144,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (($false & (X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i))))) | (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $false)) )),
0.13/0.53	  inference(boolean_simplification,[],[f143])).
0.13/0.53	thf(f145,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ ($false & (X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)))) != $true) | (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $false)) )),
0.13/0.53	  inference(boolean_simplification,[],[f144])).
0.13/0.53	thf(f146,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : (($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $false)) )),
0.13/0.53	  inference(boolean_simplification,[],[f145])).
0.13/0.53	thf(f159,definition,(
0.13/0.53	  spl0_17 <=> ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : ((((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((X0 @ X1 @ X2)) = $true) | (((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false))),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition])).
0.13/0.53	thf(f160,plain,(
0.13/0.53	  ( ! [X2 : $i,X0 : ($i > $i > $o),X1 : $i] : ((((X0 @ lSue_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((X0 @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | (((X0 @ X1 @ X2)) = $true)) ) | ~spl0_17),
0.13/0.53	  inference(avatar_component_clause,[],[f159])).
0.13/0.53	thf(f161,plain,(
0.13/0.53	  spl0_17 | ~spl0_10),
0.13/0.53	  inference(avatar_split_clause,[],[f139,f87,f159])).
0.13/0.53	thf(f163,definition,(
0.13/0.53	  spl0_18 <=> ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false)))),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition])).
0.13/0.53	thf(f165,plain,(
0.13/0.53	  ($true != ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | spl0_18),
0.13/0.53	  inference(avatar_component_clause,[],[f163])).
0.13/0.53	thf(f167,definition,(
0.13/0.53	  spl0_19 <=> ! [X0 : ($i > $i > $o)] : (((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $false)),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition])).
0.13/0.53	thf(f168,plain,(
0.13/0.53	  ( ! [X0 : ($i > $i > $o)] : ((((X0 @ (sK1 @ X0) @ (sK2 @ X0))) = $false)) ) | ~spl0_19),
0.13/0.53	  inference(avatar_component_clause,[],[f167])).
0.13/0.53	thf(f169,plain,(
0.13/0.53	  ~spl0_18 | spl0_19),
0.13/0.53	  inference(avatar_split_clause,[],[f146,f167,f163])).
0.13/0.53	thf(f186,plain,(
0.13/0.53	  ((((^[Y0 : $i]: ((^[Y1 : $i]: ($true)))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))) @ (sK2 @ (^[Y0 : $i]: ((^[Y1 : $i]: ($true))))))) = $false) | ~spl0_19),
0.13/0.53	  inference(primitive_instantiation,[],[f168])).
0.13/0.53	thf(f193,plain,(
0.13/0.53	  ($true = $false) | ~spl0_19),
0.13/0.53	  inference(beta-eta_normalization,[],[f186])).
0.13/0.53	thf(f194,plain,(
0.13/0.53	  $false | ~spl0_19),
0.13/0.53	  inference(trivial_inequality_removal,[],[f193])).
0.13/0.53	thf(f195,plain,(
0.13/0.53	  ~spl0_19),
0.13/0.53	  inference(avatar_contradiction_clause,[],[f194])).
0.13/0.53	thf(f217,plain,(
0.13/0.53	  ( ! [X0 : $i,X1 : $i] : (($true = ((likes_THFTYPE_IiioI @ X0 @ X1))) | ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | (((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false)) ) | (~spl0_1 | ~spl0_17)),
0.13/0.53	  inference(superposition,[],[f44,f160])).
0.13/0.53	thf(f253,plain,(
0.13/0.53	  ( ! [X0 : $i,X1 : $i] : ((((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) = $false) | ($true = ((likes_THFTYPE_IiioI @ X0 @ X1)))) ) | (~spl0_1 | ~spl0_17 | spl0_18)),
0.13/0.53	  inference(forward_subsumption_resolution,[],[f217,f165])).
0.13/0.53	thf(f259,definition,(
0.13/0.53	  spl0_28 <=> ! [X0 : $i,X1 : $i] : ($true = ((likes_THFTYPE_IiioI @ X0 @ X1)))),
0.13/0.53	  introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition])).
0.13/0.53	thf(f260,plain,(
0.13/0.53	  ( ! [X0 : $i,X1 : $i] : (($true = ((likes_THFTYPE_IiioI @ X0 @ X1)))) ) | ~spl0_28),
0.13/0.53	  inference(avatar_component_clause,[],[f259])).
0.13/0.53	thf(f261,plain,(
0.13/0.53	  spl0_28 | spl0_15 | ~spl0_1 | ~spl0_17 | spl0_18),
0.13/0.53	  inference(avatar_split_clause,[],[f253,f163,f159,f42,f117,f259])).
0.13/0.53	thf(f262,definition,(
0.13/0.53	  (((likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i)) != $false) | (((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (likes_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i))) != $true) | ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false)))),
0.13/0.53	  introduced(theory,[theory_tautology_sat_conflict])).
0.13/0.53	thf(f312,plain,(
0.13/0.53	  ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ (~ $true)))) | (~spl0_8 | ~spl0_28)),
0.13/0.53	  inference(superposition,[],[f79,f260])).
0.13/0.53	thf(f317,plain,(
0.13/0.53	  ($true = ((holdsDuring_THFTYPE_IiooI @ (lYearFn_THFTYPE_IiiI @ n2009_THFTYPE_i) @ $false))) | (~spl0_8 | ~spl0_28)),
0.13/0.53	  inference(boolean_simplification,[],[f312])).
0.13/0.53	thf(f324,plain,(
0.13/0.53	  $false | (~spl0_8 | spl0_18 | ~spl0_28)),
0.13/0.53	  inference(forward_subsumption_resolution,[],[f317,f165])).
0.13/0.53	thf(f325,plain,(
0.13/0.53	  ~spl0_8 | spl0_18 | ~spl0_28),
0.13/0.53	  inference(avatar_contradiction_clause,[],[f324])).
0.13/0.53	cnf(s1, plain, spl0_1, inference(sat_conversion,[],[f45])).
0.13/0.53	cnf(s6, plain, spl0_6, inference(sat_conversion,[],[f70])).
0.13/0.53	cnf(s8, plain, spl0_8, inference(sat_conversion,[],[f80])).
0.13/0.53	cnf(s14, plain, ~spl0_6 | spl0_10 | spl0_15, inference(sat_conversion,[],[f120])).
0.13/0.53	cnf(s16, plain, ~spl0_10 | spl0_17, inference(sat_conversion,[],[f161])).
0.13/0.53	cnf(s17, plain, ~spl0_18 | spl0_19, inference(sat_conversion,[],[f169])).
0.13/0.53	cnf(s20, plain, ~spl0_19, inference(sat_conversion,[],[f195])).
0.13/0.53	cnf(s25, plain, ~spl0_1 | spl0_15 | ~spl0_17 | spl0_18 | spl0_28, inference(sat_conversion,[],[f261])).
0.13/0.53	cnf(s26, plain, ~spl0_6 | ~spl0_15 | spl0_18, inference(sat_conversion,[],[f262])).
0.13/0.53	cnf(s41, plain, ~spl0_8 | spl0_18 | ~spl0_28, inference(sat_conversion,[],[f325])).
0.13/0.53	cnf(s45, plain, ~spl0_18, inference(rat,[],[s17,s20])).
0.13/0.53	cnf(s46, plain, ~spl0_28, inference(rat,[],[s41,s45,s8])).
0.13/0.53	cnf(s48, plain, ~spl0_15, inference(rat,[],[s26,s45,s6])).
0.13/0.53	cnf(s49, plain, spl0_10, inference(rat,[],[s14,s48,s6])).
0.13/0.53	cnf(s50, plain, spl0_17, inference(rat,[],[s16,s49])).
0.13/0.53	cnf(s51, plain, ~spl0_1, inference(rat,[],[s25,s46,s45,s48,s50])).
0.13/0.53	cnf(s52, plain, $false, inference(rat,[],[s1,s51])).
0.13/0.53	thf(f335,plain,(
0.13/0.53	  $false),
0.13/0.53	  inference(avatar_sat_refutation,[],[s52])).
0.13/0.53	% SZS output end Proof for theBenchmark
0.13/0.53	% (874445)------------------------------
0.13/0.53	% (874445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
0.13/0.53	% (874445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
0.13/0.53	% (874445)CaDiCaL version: 2.1.3
0.13/0.53	% (874445)Termination reason: Refutation
0.13/0.53	% (874445)Time elapsed: 0.010 s
0.13/0.53	% (874445)Peak memory usage: 13 MB
0.13/0.53	% (874445)Instructions burned: 16 (million)
0.13/0.53	% (874437)Success in time 0.045 s
0.13/0.53	% Vampire exiting
0.13/0.53	EOF