%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:37:37 AM UTC 2026
% Result : Unsatisfiable 9.68s 2.07s
% Output : Refutation 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 63 unt; 14 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 18 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 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/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f2,negated_conjecture,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f3,negated_conjecture,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f5,definition,
sF0 = apply(s,s),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f6,plain,
apply(s,s) = sF0,
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
sF1 = apply(s,k),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f8,plain,
apply(s,k) = sF1,
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
sF2 = apply(sF1,k),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f10,plain,
apply(sF1,k) = sF2,
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
sF3 = apply(sF0,sF2),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f12,plain,
apply(sF0,sF2) = sF3,
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
sF4 = apply(sF0,sF1),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f14,plain,
apply(sF0,sF1) = sF4,
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
sF5 = apply(sF3,sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f16,plain,
apply(sF3,sF4) = sF5,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF6 = apply(k,sF5),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f18,plain,
apply(k,sF5) = sF6,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF7 = apply(s,sF6),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f20,plain,
apply(s,sF6) = sF7,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF8 = apply(k,s),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f22,plain,
apply(k,s) = sF8,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF9 = apply(s,sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f24,plain,
apply(s,sF8) = sF9,
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
sF10 = apply(sF9,k),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f26,plain,
apply(sF9,k) = sF10,
inference(reorient_equations,[],[f25]) ).
fof(f27,definition,
sF11 = apply(sF7,sF10),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
fof(f28,plain,
apply(sF7,sF10) = sF11,
inference(reorient_equations,[],[f27]) ).
fof(f29,plain,
strong_fixed_point = sF11,
inference(definition_folding,[],[f3,f28,f26,f24,f22,f20,f18,f16,f14,f8,f6,f12,f10,f8,f6]) ).
fof(f30,definition,
sF12 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
fof(f31,plain,
apply(strong_fixed_point,fixed_pt) = sF12,
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
sF13 = apply(fixed_pt,sF12),
introduced(definition,[new_symbols(definition,[sF13])],[function_definition]) ).
fof(f33,plain,
apply(fixed_pt,sF12) = sF13,
inference(reorient_equations,[],[f32]) ).
fof(f34,plain,
sF12 != sF13,
inference(definition_folding,[],[f4,f33,f31,f31]) ).
fof(f35,plain,
strong_fixed_point = apply(sF7,sF10),
inference(forward_demodulation,[],[f28,f29]) ).
fof(f36,plain,
! [X2,X0,X1] : apply(apply(X1,X2),apply(apply(X0,X1),X2)) = apply(apply(apply(apply(s,s),X0),X1),X2),
inference(superposition,[],[f1,f1]) ).
fof(f37,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(s,apply(k,X0)),X1),X2),
inference(superposition,[],[f1,f2]) ).
fof(f44,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[],[f2,f1]) ).
fof(f45,plain,
! [X0,X1] : apply(apply(sF1,X0),X1) = X1,
inference(forward_demodulation,[],[f44,f8]) ).
fof(f47,plain,
! [X2,X0,X1] : apply(apply(X1,X2),apply(apply(X0,X1),X2)) = apply(apply(apply(sF0,X0),X1),X2),
inference(forward_demodulation,[],[f36,f6]) ).
fof(f52,plain,
! [X0,X1] : apply(apply(s,X1),apply(X0,X1)) = apply(apply(sF0,X0),X1),
inference(superposition,[],[f1,f6]) ).
fof(f56,plain,
! [X0] : apply(sF2,X0) = X0,
inference(superposition,[],[f45,f10]) ).
fof(f59,plain,
! [X0] : s = apply(sF8,X0),
inference(superposition,[],[f2,f22]) ).
fof(f60,plain,
! [X0,X1] : apply(apply(sF8,X1),apply(X0,X1)) = apply(apply(sF9,X0),X1),
inference(superposition,[],[f1,f24]) ).
fof(f61,plain,
! [X0,X1] : apply(s,apply(X0,X1)) = apply(apply(sF9,X0),X1),
inference(forward_demodulation,[],[f60,f59]) ).
fof(f62,plain,
! [X0] : apply(s,apply(k,X0)) = apply(sF10,X0),
inference(superposition,[],[f61,f26]) ).
fof(f67,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(sF10,X0),X1),X2),
inference(backward_demodulation,[],[f37,f62]) ).
fof(f73,plain,
! [X0] : sF5 = apply(sF6,X0),
inference(superposition,[],[f2,f18]) ).
fof(f74,plain,
! [X0,X1] : apply(apply(sF6,X1),apply(X0,X1)) = apply(apply(sF7,X0),X1),
inference(superposition,[],[f1,f20]) ).
fof(f75,plain,
! [X0,X1] : apply(apply(sF7,X0),X1) = apply(sF5,apply(X0,X1)),
inference(forward_demodulation,[],[f74,f73]) ).
fof(f103,plain,
! [X0] : apply(apply(s,X0),X0) = apply(apply(sF0,sF2),X0),
inference(superposition,[],[f52,f56]) ).
fof(f112,plain,
! [X0] : apply(apply(s,X0),X0) = apply(sF3,X0),
inference(forward_demodulation,[],[f103,f12]) ).
fof(f128,plain,
! [X0,X1] : apply(apply(X0,X1),apply(X0,X1)) = apply(apply(sF3,X0),X1),
inference(superposition,[],[f1,f112]) ).
fof(f190,plain,
! [X0,X1] : apply(apply(X1,X0),X0) = apply(apply(apply(sF0,sF1),X1),X0),
inference(superposition,[],[f47,f45]) ).
fof(f223,plain,
! [X0,X1] : apply(apply(X1,X0),X0) = apply(apply(sF4,X1),X0),
inference(forward_demodulation,[],[f190,f14]) ).
fof(f299,plain,
! [X0,X1] : apply(X0,apply(X1,X1)) = apply(apply(sF4,apply(sF10,X0)),X1),
inference(superposition,[],[f67,f223]) ).
fof(f331,plain,
! [X0] : apply(sF5,apply(sF10,X0)) = apply(strong_fixed_point,X0),
inference(superposition,[],[f75,f35]) ).
fof(f1750,plain,
! [X0] : apply(apply(sF3,sF4),apply(sF10,X0)) = apply(X0,apply(apply(sF3,sF4),apply(sF10,X0))),
inference(superposition,[],[f299,f128]) ).
fof(f1865,plain,
! [X0] : apply(sF5,apply(sF10,X0)) = apply(X0,apply(sF5,apply(sF10,X0))),
inference(forward_demodulation,[],[f1750,f16]) ).
fof(f1962,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[],[f1865,f331]) ).
fof(f2086,plain,
sF12 = apply(fixed_pt,sF12),
inference(superposition,[],[f1962,f31]) ).
fof(f2158,plain,
sF12 = sF13,
inference(backward_demodulation,[],[f33,f2086]) ).
fof(f2162,plain,
$false,
inference(forward_subsumption_resolution,[],[f2158,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n003.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:31:12 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.45/1.97 % (2045166)Detected a unit-equality problem, will run specialized UEQ schedule.
% 8.45/1.97 % (2045278)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=894153961:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 8.45/1.97 % (2045286)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=952579824:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 8.45/1.97 % (2045283)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2040947727:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 8.45/1.97 % (2045281)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=1358002246:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 8.45/1.97 % (2045287)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2048788262:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 8.45/1.97 % (2045284)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1144354001:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 8.45/1.97 % (2045282)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3991039914:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 8.45/1.97 % (2045283)Instruction limit reached!
% 8.45/1.97 % (2045283)------------------------------
% 8.45/1.97 % (2045283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.45/1.97 % (2045283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.45/1.97 % (2045283)CaDiCaL version: 2.1.3
% 8.45/1.97 % (2045283)Termination reason: Instruction limit
% 8.45/1.97 % (2045283)Termination phase: Saturation
% 8.45/1.97 % (2045283)Time elapsed: 0.079 s
% 8.45/1.97 % (2045283)Peak memory usage: 89 MB
% 8.45/1.97 % (2045283)Instructions burned: 137 (million)
% 8.45/1.97 % (2045284)Instruction limit reached!
% 8.45/1.97 % (2045284)------------------------------
% 8.45/1.97 % (2045284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.45/1.97 % (2045284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.45/1.97 % (2045284)CaDiCaL version: 2.1.3
% 8.45/1.97 % (2045284)Termination reason: Instruction limit
% 8.45/1.97 % (2045284)Termination phase: Saturation
% 8.45/1.97 % (2045284)Time elapsed: 0.098 s
% 8.45/1.97 % (2045284)Peak memory usage: 89 MB
% 8.45/1.97 % (2045284)Instructions burned: 181 (million)
% 8.45/1.97 % (2045286)Instruction limit reached!
% 8.45/1.97 % (2045286)------------------------------
% 8.45/1.97 % (2045286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.45/1.97 % (2045286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.45/1.97 % (2045286)CaDiCaL version: 2.1.3
% 8.45/1.97 % (2045286)Termination reason: Instruction limit
% 8.45/1.97 % (2045286)Termination phase: Saturation
% 8.45/1.97 % (2045286)Time elapsed: 0.173 s
% 8.45/1.97 % (2045286)Peak memory usage: 91 MB
% 8.45/1.97 % (2045286)Instructions burned: 258 (million)
% 8.45/1.97 % (2045330)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2582858542:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 8.45/1.97 % (2045331)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=999331623:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 8.45/1.97 % (2045357)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2642063465:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 8.45/1.97 % (2045357)Instruction limit reached!
% 8.45/1.97 % (2045357)------------------------------
% 8.45/1.97 % (2045357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.45/1.97 % (2045357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.45/1.97 % (2045357)CaDiCaL version: 2.1.3
% 8.45/1.97 % (2045357)Termination reason: Instruction limit
% 8.45/1.97 % (2045357)Termination phase: Saturation
% 8.45/1.97 % (2045357)Time elapsed: 0.118 s
% 9.68/2.07 % (2045357)Peak memory usage: 89 MB
% 9.68/2.07 % (2045357)Instructions burned: 215 (million)
% 9.68/2.07 % (2045441)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=4119117890: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)
% 9.68/2.07 % (2045287)Instruction limit reached!
% 9.68/2.07 % (2045287)------------------------------
% 9.68/2.07 % (2045287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.07 % (2045287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.07 % (2045287)CaDiCaL version: 2.1.3
% 9.68/2.07 % (2045287)Termination reason: Instruction limit
% 9.68/2.07 % (2045287)Termination phase: Saturation
% 9.68/2.07 % (2045287)Time elapsed: 0.632 s
% 9.68/2.07 % (2045287)Peak memory usage: 96 MB
% 9.68/2.07 % (2045287)Instructions burned: 1187 (million)
% 9.68/2.07 % (2045441)Instruction limit reached!
% 9.68/2.07 % (2045441)------------------------------
% 9.68/2.07 % (2045441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.07 % (2045441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.07 % (2045441)CaDiCaL version: 2.1.3
% 9.68/2.07 % (2045441)Termination reason: Instruction limit
% 9.68/2.07 % (2045441)Termination phase: Saturation
% 9.68/2.07 % (2045441)Time elapsed: 0.177 s
% 9.68/2.07 % (2045441)Peak memory usage: 91 MB
% 9.68/2.07 % (2045441)Instructions burned: 318 (million)
% 9.68/2.07 % (2045486)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=3994631144:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 9.68/2.07 % (2045282)First to succeed.
% 9.68/2.07 % (2045282)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2045166"
% 9.68/2.07 % (2045491)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3004841847:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 9.68/2.07 % (2045282)Refutation found. Thanks to Tanya!
% 9.68/2.07 % SZS status Unsatisfiable for theBenchmark
% 9.68/2.07 % SZS output start Proof for theBenchmark
% See solution above
% 9.68/2.07 % (2045282)------------------------------
% 9.68/2.07 % (2045282)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.07 % (2045282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.07 % (2045282)CaDiCaL version: 2.1.3
% 9.68/2.07 % (2045282)Termination reason: Refutation
% 9.68/2.07 % (2045282)Time elapsed: 0.853 s
% 9.68/2.07 % (2045282)Peak memory usage: 132 MB
% 9.68/2.07 % (2045282)Instructions burned: 1333 (million)
% 9.68/2.07 % (2045282)------------------------------
% 9.68/2.07 % (2045282)------------------------------
% 9.68/2.07 % (2045166)Success in time 1.301 s
% 9.68/2.07 % Vampire exiting
%------------------------------------------------------------------------------