%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:37:33 AM UTC 2026
% Result : Unsatisfiable 4.91s 1.54s
% Output : Refutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 19
% Syntax : Number of formulae : 56 ( 56 unt; 14 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 9 con; 0-3 aty)
% Number of variables : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,negated_conjecture,
! [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(f4,negated_conjecture,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i_definition) ).
fof(f5,negated_conjecture,
! [X0] : weak_fixed_point(X0) = apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f6,negated_conjecture,
weak_fixed_point(fixed_pt) != apply(fixed_pt,weak_fixed_point(fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f7,plain,
apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i)) != apply(fixed_pt,apply(apply(apply(s,apply(b,fixed_pt)),i),apply(apply(s,apply(b,fixed_pt)),i))),
inference(definition_unfolding,[],[f6,f5,f5]) ).
fof(f8,definition,
! [X0] : sF0(X0) = apply(s,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X0] : apply(s,X0) = sF0(X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0,X1] : sF1(X0,X1) = apply(sF0(X0),X1),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
! [X0,X1] : apply(sF0(X0),X1) = sF1(X0,X1),
inference(reorient_equations,[],[f10]) ).
fof(f12,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = apply(sF1(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f13,plain,
! [X2,X0,X1] : apply(sF1(X0,X1),X2) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X0,X1] : sF3(X0,X2,X1) = apply(apply(X0,X2),apply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f15,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = sF3(X0,X2,X1),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X2,X0,X1] : sF2(X0,X1,X2) = sF3(X0,X2,X1),
inference(definition_folding,[],[f1,f15,f13,f11,f9]) ).
fof(f17,definition,
! [X0] : sF4(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f18,plain,
! [X0] : apply(b,X0) = sF4(X0),
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
! [X0,X1] : sF5(X0,X1) = apply(sF4(X0),X1),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f20,plain,
! [X0,X1] : apply(sF4(X0),X1) = sF5(X0,X1),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
! [X2,X0,X1] : sF6(X0,X1,X2) = apply(sF5(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f22,plain,
! [X2,X0,X1] : apply(sF5(X0,X1),X2) = sF6(X0,X1,X2),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
! [X2,X0,X1] : sF7(X0,X1,X2) = apply(X0,apply(X1,X2)),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f24,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF7(X0,X1,X2),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X2,X0,X1] : sF6(X0,X1,X2) = sF7(X0,X1,X2),
inference(definition_folding,[],[f2,f24,f22,f20,f18]) ).
fof(f35,definition,
! [X0] : sF12(X0) = apply(i,X0),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f36,plain,
! [X0] : apply(i,X0) = sF12(X0),
inference(reorient_equations,[],[f35]) ).
fof(f37,plain,
! [X0] : sF12(X0) = X0,
inference(definition_folding,[],[f4,f36]) ).
fof(f38,definition,
sF13 = apply(b,fixed_pt),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f39,plain,
apply(b,fixed_pt) = sF13,
inference(reorient_equations,[],[f38]) ).
fof(f40,definition,
sF14 = apply(s,sF13),
introduced(definition,[new_symbols(definition,[sF14])],[function_definition]) ).
fof(f41,plain,
apply(s,sF13) = sF14,
inference(reorient_equations,[],[f40]) ).
fof(f42,definition,
sF15 = apply(sF14,i),
introduced(definition,[new_symbols(definition,[sF15])],[function_definition]) ).
fof(f43,plain,
apply(sF14,i) = sF15,
inference(reorient_equations,[],[f42]) ).
fof(f44,definition,
sF16 = apply(sF15,sF15),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f45,plain,
apply(sF15,sF15) = sF16,
inference(reorient_equations,[],[f44]) ).
fof(f46,definition,
sF17 = apply(fixed_pt,sF16),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f47,plain,
apply(fixed_pt,sF16) = sF17,
inference(reorient_equations,[],[f46]) ).
fof(f48,plain,
sF16 != sF17,
inference(definition_folding,[],[f7,f47,f45,f43,f41,f39,f43,f41,f39,f45,f43,f41,f39,f43,f41,f39]) ).
fof(f49,plain,
! [X0] : apply(i,X0) = X0,
inference(forward_demodulation,[],[f37,f36]) ).
fof(f51,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = sF6(X0,X1,X2),
inference(forward_demodulation,[],[f25,f24]) ).
fof(f52,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = sF2(X0,X1,X2),
inference(forward_demodulation,[],[f16,f15]) ).
fof(f54,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(sF5(X0,X1),X2),
inference(forward_demodulation,[],[f51,f22]) ).
fof(f55,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = apply(sF1(X0,X1),X2),
inference(forward_demodulation,[],[f52,f13]) ).
fof(f57,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(sF4(X0),X1),X2),
inference(forward_demodulation,[],[f54,f20]) ).
fof(f58,plain,
! [X2,X0,X1] : apply(apply(X0,X2),apply(X1,X2)) = apply(apply(sF0(X0),X1),X2),
inference(forward_demodulation,[],[f55,f11]) ).
fof(f60,plain,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(forward_demodulation,[],[f57,f18]) ).
fof(f61,plain,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(forward_demodulation,[],[f58,f9]) ).
fof(f81,plain,
! [X0,X1] : apply(fixed_pt,apply(X0,X1)) = apply(apply(sF13,X0),X1),
inference(superposition,[],[f60,f39]) ).
fof(f146,plain,
! [X0,X1] : apply(apply(apply(s,X1),i),X0) = apply(apply(X1,X0),X0),
inference(superposition,[],[f61,f49]) ).
fof(f291,plain,
! [X0] : apply(fixed_pt,apply(X0,X0)) = apply(apply(apply(s,sF13),i),X0),
inference(superposition,[],[f81,f146]) ).
fof(f297,plain,
! [X0] : apply(apply(sF14,i),X0) = apply(fixed_pt,apply(X0,X0)),
inference(forward_demodulation,[],[f291,f41]) ).
fof(f307,plain,
! [X0] : apply(fixed_pt,apply(X0,X0)) = apply(sF15,X0),
inference(forward_demodulation,[],[f297,f43]) ).
fof(f318,plain,
sF16 = apply(fixed_pt,sF16),
inference(superposition,[],[f307,f45]) ).
fof(f324,plain,
sF16 = sF17,
inference(forward_demodulation,[],[f318,f47]) ).
fof(f331,plain,
sF16 != sF16,
inference(superposition,[],[f48,f324]) ).
fof(f332,plain,
$false,
inference(trivial_inequality_removal,[],[f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-4 : TPTP v9.3.1. Bugfixed v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 21:28:10 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 4.91/1.54 % (220877)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.91/1.54 % (220933)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1811725872:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.91/1.54 % (220932)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1051655387:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.91/1.54 % (220930)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=2837481242:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.91/1.54 % (220931)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=1923925791:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.91/1.54 % (220933)Instruction limit reached!
% 4.91/1.54 % (220933)------------------------------
% 4.91/1.54 % (220933)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.54 % (220933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.54 % (220933)CaDiCaL version: 2.1.3
% 4.91/1.54 % (220933)Termination reason: Instruction limit
% 4.91/1.54 % (220933)Termination phase: Saturation
% 4.91/1.54 % (220933)Time elapsed: 0.044 s
% 4.91/1.54 % (220933)Peak memory usage: 89 MB
% 4.91/1.54 % (220933)Instructions burned: 139 (million)
% 4.91/1.54 % (220934)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2448783904:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.91/1.54 % (220935)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=334890469:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.91/1.54 % (220936)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3443806619:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.91/1.54 % (220934)First to succeed.
% 4.91/1.54 % (220934)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-220877"
% 4.91/1.54 % (220935)Also succeeded, but the first one will report.
% 4.91/1.54 % (220941)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3023368924:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 4.91/1.54 % (220934)Refutation found. Thanks to Tanya!
% 4.91/1.54 % SZS status Unsatisfiable for theBenchmark
% 4.91/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 4.91/1.55 % (220934)------------------------------
% 4.91/1.55 % (220934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.91/1.55 % (220934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.91/1.55 % (220934)CaDiCaL version: 2.1.3
% 4.91/1.55 % (220934)Termination reason: Refutation
% 4.91/1.55 % (220934)Time elapsed: 0.015 s
% 4.91/1.55 % (220934)Peak memory usage: 88 MB
% 4.91/1.55 % (220934)Instructions burned: 23 (million)
% 4.91/1.55 % (220934)------------------------------
% 4.91/1.55 % (220934)------------------------------
% 4.91/1.55 % (220877)Success in time 0.606 s
% 4.91/1.55 % Vampire exiting
%------------------------------------------------------------------------------