%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL042-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:41 AM UTC 2026
% Result : Unsatisfiable 30.24s 5.11s
% Output : Refutation 30.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w1_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f5,plain,
! [X2,X0,X1] : apply(apply(w1,X2),apply(apply(b,X0),X1)) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f2,f1]) ).
fof(f11,plain,
! [X0,X1] : apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(superposition,[],[f3,f1]) ).
fof(f12,plain,
! [X2,X0,X1] : apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1)))))) != apply(f(apply(apply(b,X2),apply(apply(b,X0),X1))),apply(X2,apply(X0,apply(X1,f(apply(apply(b,X2),apply(apply(b,X0),X1))))))),
inference(superposition,[],[f11,f1]) ).
fof(f32,plain,
! [X0,X1] : apply(apply(X0,apply(X1,X0)),apply(X1,X0)) = apply(apply(w1,X0),apply(apply(b,w1),X1)),
inference(superposition,[],[f2,f5]) ).
fof(f33,plain,
! [X2,X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(superposition,[],[f1,f5]) ).
fof(f98,plain,
! [X0] : apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))) = apply(X0,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0))))),
inference(superposition,[],[f33,f32]) ).
fof(f153,plain,
! [X2,X3,X0,X1] : apply(X3,apply(X0,apply(X1,apply(X2,f(apply(apply(b,X3),apply(apply(b,apply(apply(b,X0),X1)),X2))))))) != apply(f(apply(apply(b,X3),apply(apply(b,apply(apply(b,X0),X1)),X2))),apply(X3,apply(X0,apply(X1,apply(X2,f(apply(apply(b,X3),apply(apply(b,apply(apply(b,X0),X1)),X2)))))))),
inference(superposition,[],[f12,f1]) ).
fof(f176,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,f(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(apply(b,apply(b,w1)),b)),b))))))) != apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,f(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(apply(b,apply(b,w1)),b)),b))))))),
inference(superposition,[],[f153,f98]) ).
fof(f177,plain,
$false,
inference(trivial_inequality_removal,[],[f176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL042-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:33:12 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 30.24/5.11 % (94899)Detected a unit-equality problem, will run specialized UEQ schedule.
% 30.24/5.11 % (94919)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=928890208:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 30.24/5.11 % (94917)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1856478087:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 30.24/5.11 % (94918)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2304092485:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 30.24/5.11 % (94915)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=2249946219:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 30.24/5.11 % (94916)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3332176429:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 30.24/5.11 % (94921)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4156639463:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 30.24/5.11 % (94919)Instruction limit reached!
% 30.24/5.11 % (94919)------------------------------
% 30.24/5.11 % (94919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (94919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (94919)CaDiCaL version: 2.1.3
% 30.24/5.11 % (94919)Termination reason: Instruction limit
% 30.24/5.11 % (94919)Termination phase: Saturation
% 30.24/5.11 % (94919)Time elapsed: 0.055 s
% 30.24/5.11 % (94919)Peak memory usage: 89 MB
% 30.24/5.11 % (94919)Instructions burned: 181 (million)
% 30.24/5.11 % (94920)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2229138968:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 30.24/5.11 % (94918)Instruction limit reached!
% 30.24/5.11 % (94918)------------------------------
% 30.24/5.11 % (94918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (94918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (94918)CaDiCaL version: 2.1.3
% 30.24/5.11 % (94918)Termination reason: Instruction limit
% 30.24/5.11 % (94918)Termination phase: Saturation
% 30.24/5.11 % (94918)Time elapsed: 0.085 s
% 30.24/5.11 % (94918)Peak memory usage: 89 MB
% 30.24/5.11 % (94918)Instructions burned: 137 (million)
% 30.24/5.11 % (94929)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2413566478:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 30.24/5.11 % (94952)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1173471523:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 30.24/5.11 % (94920)Instruction limit reached!
% 30.24/5.11 % (94920)------------------------------
% 30.24/5.11 % (94920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (94920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (94920)CaDiCaL version: 2.1.3
% 30.24/5.11 % (94920)Termination reason: Instruction limit
% 30.24/5.11 % (94920)Termination phase: Saturation
% 30.24/5.11 % (94920)Time elapsed: 0.172 s
% 30.24/5.11 % (94920)Peak memory usage: 91 MB
% 30.24/5.11 % (94920)Instructions burned: 258 (million)
% 30.24/5.11 % (95002)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3788489504:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 30.24/5.11 % (95002)Instruction limit reached!
% 30.24/5.11 % (95002)------------------------------
% 30.24/5.11 % (95002)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (95002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (95002)CaDiCaL version: 2.1.3
% 30.24/5.11 % (95002)Termination reason: Instruction limit
% 30.24/5.11 % (95002)Termination phase: Saturation
% 30.24/5.11 % (95002)Time elapsed: 0.135 s
% 30.24/5.11 % (95002)Peak memory usage: 90 MB
% 30.24/5.11 % (95002)Instructions burned: 216 (million)
% 30.24/5.11 % (95040)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1936223266:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 30.24/5.11 % (94921)Instruction limit reached!
% 30.24/5.11 % (94921)------------------------------
% 30.24/5.11 % (94921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (94921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (94921)CaDiCaL version: 2.1.3
% 30.24/5.11 % (94921)Termination reason: Instruction limit
% 30.24/5.11 % (94921)Termination phase: Saturation
% 30.24/5.11 % (94921)Time elapsed: 0.623 s
% 30.24/5.11 % (94921)Peak memory usage: 95 MB
% 30.24/5.11 % (94921)Instructions burned: 1187 (million)
% 30.24/5.11 % (95089)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2618441817:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2992 on theBenchmark for (2992ds/12125Mi)
% 30.24/5.11 % (95040)Instruction limit reached!
% 30.24/5.11 % (95040)------------------------------
% 30.24/5.11 % (95040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (95040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (95040)CaDiCaL version: 2.1.3
% 30.24/5.11 % (95040)Termination reason: Instruction limit
% 30.24/5.11 % (95040)Termination phase: Saturation
% 30.24/5.11 % (95040)Time elapsed: 0.198 s
% 30.24/5.11 % (95040)Peak memory usage: 94 MB
% 30.24/5.11 % (95040)Instructions burned: 318 (million)
% 30.24/5.11 % (95091)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=1163041814:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 30.24/5.11 % (94929)Instruction limit reached!
% 30.24/5.11 % (94929)------------------------------
% 30.24/5.11 % (94929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (94929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (94929)CaDiCaL version: 2.1.3
% 30.24/5.11 % (94929)Termination reason: Instruction limit
% 30.24/5.11 % (94929)Termination phase: Saturation
% 30.24/5.11 % (94929)Time elapsed: 1.036 s
% 30.24/5.11 % (94929)Peak memory usage: 141 MB
% 30.24/5.11 % (94929)Instructions burned: 2052 (million)
% 30.24/5.11 % (95093)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=395154843:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2987 on theBenchmark for (2987ds/14534Mi)
% 30.24/5.11 % (95091)Instruction limit reached!
% 30.24/5.11 % (95091)------------------------------
% 30.24/5.11 % (95091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (95091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (95091)CaDiCaL version: 2.1.3
% 30.24/5.11 % (95091)Termination reason: Instruction limit
% 30.24/5.11 % (95091)Termination phase: Saturation
% 30.24/5.11 % (95091)Time elapsed: 1.819 s
% 30.24/5.11 % (95091)Peak memory usage: 130 MB
% 30.24/5.11 % (95091)Instructions burned: 2836 (million)
% 30.24/5.11 % (95095)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:sas=cadical:sp=reverse_frequency:bsr=on:alpa=false:sac=on:random_seed=1793390729:i=11832:s2at=3:bs=on:bd=preordered:fsd=on_2970 on theBenchmark for (2970ds/11832Mi)
% 30.24/5.11 % (94952)Instruction limit reached!
% 30.24/5.11 % (94952)------------------------------
% 30.24/5.11 % (94952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (94952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (94952)CaDiCaL version: 2.1.3
% 30.24/5.11 % (94952)Termination reason: Instruction limit
% 30.24/5.11 % (94952)Termination phase: Saturation
% 30.24/5.11 % (94952)Time elapsed: 2.782 s
% 30.24/5.11 % (94952)Peak memory usage: 169 MB
% 30.24/5.11 % (94952)Instructions burned: 4949 (million)
% 30.24/5.11 % (95097)lrs+10_1_to=lpo:ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:drc=off:fde=unused:sp=const_min:spb=goal:fd=preordered:random_seed=3198483239:i=2279:fgj=on:bd=all_2968 on theBenchmark for (2968ds/2279Mi)
% 30.24/5.11 % (95097)First to succeed.
% 30.24/5.11 % (95097)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-94899"
% 30.24/5.11 % (95097)Refutation found. Thanks to Tanya!
% 30.24/5.11 % SZS status Unsatisfiable for theBenchmark
% 30.24/5.11 % SZS output start Proof for theBenchmark
% See solution above
% 30.24/5.11 % (95097)------------------------------
% 30.24/5.11 % (95097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 30.24/5.11 % (95097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 30.24/5.11 % (95097)CaDiCaL version: 2.1.3
% 30.24/5.11 % (95097)Termination reason: Refutation
% 30.24/5.11 % (95097)Time elapsed: 0.651 s
% 30.24/5.11 % (95097)Peak memory usage: 128 MB
% 30.24/5.11 % (95097)Instructions burned: 995 (million)
% 30.24/5.11 % (95097)------------------------------
% 30.24/5.11 % (95097)------------------------------
% 30.24/5.11 % (94899)Success in time 4.177 s
% 30.24/5.11 % Vampire exiting
%------------------------------------------------------------------------------