%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 09:37:53 AM UTC 2026
% Result : Unsatisfiable 7.86s 1.79s
% Output : Refutation 7.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 18 unt; 3 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
fof(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f5,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC2c) ).
fof(f6,definition,
sF0 = k(b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f7,plain,
k(b) = sF0,
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
sF1 = k(sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f9,plain,
k(sF0) = sF1,
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
sF2 = apply(abstraction,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f11,plain,
apply(abstraction,sF1) = sF2,
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
sF1 != sF2,
inference(definition_folding,[],[f5,f11,f9,f7,f9,f7]) ).
fof(f14,plain,
! [X0] : b = apply(sF0,X0),
inference(superposition,[],[f1,f7]) ).
fof(f15,plain,
! [X0] : sF0 = apply(sF1,X0),
inference(superposition,[],[f1,f9]) ).
fof(f29,plain,
! [X0,X1] : apply(apply(apply(abstraction,sF1),X0),X1) = apply(sF0,apply(X0,X1)),
inference(superposition,[],[f2,f15]) ).
fof(f36,plain,
! [X0,X1] : b = apply(apply(apply(abstraction,sF1),X0),X1),
inference(forward_demodulation,[],[f29,f14]) ).
fof(f38,plain,
! [X0,X1] : b = apply(apply(sF2,X0),X1),
inference(forward_demodulation,[],[f36,f11]) ).
fof(f47,plain,
! [X0,X1] :
( b != apply(X1,n(apply(sF2,X0),X1))
| apply(sF2,X0) = X1 ),
inference(superposition,[],[f3,f38]) ).
fof(f62,plain,
! [X0] :
( b != b
| sF0 = apply(sF2,X0) ),
inference(superposition,[],[f47,f14]) ).
fof(f64,plain,
! [X0] : sF0 = apply(sF2,X0),
inference(trivial_inequality_removal,[],[f62]) ).
fof(f90,plain,
! [X0] :
( sF0 != apply(X0,n(X0,sF2))
| sF2 = X0 ),
inference(superposition,[],[f3,f64]) ).
fof(f100,plain,
( sF0 != sF0
| sF1 = sF2 ),
inference(superposition,[],[f90,f15]) ).
fof(f101,plain,
sF1 = sF2,
inference(trivial_inequality_removal,[],[f100]) ).
fof(f102,plain,
$false,
inference(forward_subsumption_resolution,[],[f101,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:34:46 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 6.32/1.69 % (3809145)Input is clausal, will run a generic CNF schedule.
% 6.32/1.69 % (3809153)lrs+10_1_sil=8000:sp=occurrence:random_seed=2091925725:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.32/1.69 % (3809150)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1276638960:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.32/1.69 % (3809153)Instruction limit reached!
% 6.32/1.69 % (3809153)------------------------------
% 6.32/1.69 % (3809153)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.69 % (3809153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.69 % (3809153)CaDiCaL version: 2.1.3
% 6.32/1.69 % (3809153)Termination reason: Instruction limit
% 6.32/1.69 % (3809153)Termination phase: Saturation
% 6.32/1.69 % (3809153)Time elapsed: 0.038 s
% 6.32/1.69 % (3809153)Peak memory usage: 89 MB
% 6.32/1.69 % (3809153)Instructions burned: 109 (million)
% 6.32/1.69 % (3809155)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3535539073:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.32/1.69 % (3809152)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3469196278:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.32/1.69 % (3809151)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1713685166:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.32/1.69 % (3809156)dis-21_1_sil=8000:lcm=predicate:random_seed=3897905589:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.32/1.69 % (3809154)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1313268669:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.32/1.69 % (3809156)Refutation not found, incomplete strategy
% 6.32/1.69 % (3809156)------------------------------
% 6.32/1.69 % (3809156)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.69 % (3809156)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.69 % (3809156)CaDiCaL version: 2.1.3
% 6.32/1.69 % (3809156)Termination reason: Refutation not found, incomplete strategy
% 6.32/1.69 % (3809156)Time elapsed: 0.001 s
% 6.32/1.69 % (3809156)Peak memory usage: 88 MB
% 6.32/1.69 % (3809154)Instruction limit reached!
% 6.32/1.69 % (3809154)------------------------------
% 6.32/1.69 % (3809154)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.69 % (3809154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.69 % (3809154)CaDiCaL version: 2.1.3
% 6.32/1.69 % (3809154)Termination reason: Instruction limit
% 6.32/1.69 % (3809154)Termination phase: Saturation
% 6.32/1.69 % (3809154)Time elapsed: 0.073 s
% 6.32/1.69 % (3809154)Peak memory usage: 88 MB
% 6.32/1.69 % (3809154)Instructions burned: 115 (million)
% 6.32/1.69 % (3809155)Instruction limit reached!
% 6.32/1.69 % (3809155)------------------------------
% 6.32/1.69 % (3809155)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.69 % (3809155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.70 % (3809155)CaDiCaL version: 2.1.3
% 6.32/1.70 % (3809155)Termination reason: Instruction limit
% 6.32/1.70 % (3809155)Termination phase: Saturation
% 6.32/1.70 % (3809155)Time elapsed: 0.104 s
% 6.32/1.70 % (3809155)Peak memory usage: 89 MB
% 6.32/1.70 % (3809155)Instructions burned: 180 (million)
% 6.32/1.70 % (3809159)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=3012159161:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.32/1.70 % (3809159)Refutation not found, incomplete strategy
% 6.32/1.70 % (3809159)------------------------------
% 6.32/1.70 % (3809159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.32/1.70 % (3809159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.32/1.70 % (3809159)CaDiCaL version: 2.1.3
% 6.32/1.70 % (3809159)Termination reason: Refutation not found, incomplete strategy
% 6.32/1.70 % (3809159)Time elapsed: 0.0000 s
% 6.32/1.70 % (3809159)Peak memory usage: 88 MB
% 6.32/1.70 % (3809165)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=92241132:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 7.86/1.79 % (3809156)------------------------------
% 7.86/1.79 % (3809156)------------------------------
% 7.86/1.79 % (3809159)------------------------------
% 7.86/1.79 % (3809159)------------------------------
% 7.86/1.79 % (3809167)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1505149960:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 7.86/1.79 % (3809167)Refutation not found, incomplete strategy
% 7.86/1.79 % (3809167)------------------------------
% 7.86/1.79 % (3809167)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809167)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809167)Termination reason: Refutation not found, incomplete strategy
% 7.86/1.79 % (3809167)Time elapsed: 0.001 s
% 7.86/1.79 % (3809167)Peak memory usage: 87 MB
% 7.86/1.79 % (3809165)Instruction limit reached!
% 7.86/1.79 % (3809165)------------------------------
% 7.86/1.79 % (3809165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809165)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809165)Termination reason: Instruction limit
% 7.86/1.79 % (3809165)Termination phase: Saturation
% 7.86/1.79 % (3809165)Time elapsed: 0.092 s
% 7.86/1.79 % (3809165)Peak memory usage: 94 MB
% 7.86/1.79 % (3809165)Instructions burned: 191 (million)
% 7.86/1.79 % (3809170)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1331497946:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 7.86/1.79 % (3809169)lrs+10_64_to=lpo:sil=8000:random_seed=1018925135:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 7.86/1.79 % (3809170)Instruction limit reached!
% 7.86/1.79 % (3809170)------------------------------
% 7.86/1.79 % (3809170)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809170)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809170)Termination reason: Instruction limit
% 7.86/1.79 % (3809170)Termination phase: Saturation
% 7.86/1.79 % (3809170)Time elapsed: 0.067 s
% 7.86/1.79 % (3809170)Peak memory usage: 91 MB
% 7.86/1.79 % (3809170)Instructions burned: 196 (million)
% 7.86/1.79 % (3809172)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3004235031:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 7.86/1.79 % (3809169)Instruction limit reached!
% 7.86/1.79 % (3809169)------------------------------
% 7.86/1.79 % (3809169)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809169)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809169)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809169)Termination reason: Instruction limit
% 7.86/1.79 % (3809169)Termination phase: Saturation
% 7.86/1.79 % (3809169)Time elapsed: 0.078 s
% 7.86/1.79 % (3809169)Peak memory usage: 89 MB
% 7.86/1.79 % (3809169)Instructions burned: 127 (million)
% 7.86/1.79 % (3809167)------------------------------
% 7.86/1.79 % (3809167)------------------------------
% 7.86/1.79 % (3809175)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3119884795:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 7.86/1.79 % (3809172)Instruction limit reached!
% 7.86/1.79 % (3809172)------------------------------
% 7.86/1.79 % (3809172)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809172)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809172)Termination reason: Instruction limit
% 7.86/1.79 % (3809172)Termination phase: Saturation
% 7.86/1.79 % (3809172)Time elapsed: 0.099 s
% 7.86/1.79 % (3809172)Peak memory usage: 90 MB
% 7.86/1.79 % (3809172)Instructions burned: 157 (million)
% 7.86/1.79 % (3809150)First to succeed.
% 7.86/1.79 % (3809150)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3809145"
% 7.86/1.79 % (3809151)Also succeeded, but the first one will report.
% 7.86/1.79 % (3809152)Also succeeded, but the first one will report.
% 7.86/1.79 % (3809177)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2810054298:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 7.86/1.79 % (3809178)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2270815516:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 7.86/1.79 % (3809178)Refutation not found, incomplete strategy
% 7.86/1.79 % (3809178)------------------------------
% 7.86/1.79 % (3809178)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809178)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809178)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809178)Termination reason: Refutation not found, incomplete strategy
% 7.86/1.79 % (3809178)Time elapsed: 0.001 s
% 7.86/1.79 % (3809178)Peak memory usage: 87 MB
% 7.86/1.79 % (3809177)Instruction limit reached!
% 7.86/1.79 % (3809177)------------------------------
% 7.86/1.79 % (3809177)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809177)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809177)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809177)Termination reason: Instruction limit
% 7.86/1.79 % (3809177)Termination phase: Saturation
% 7.86/1.79 % (3809177)Time elapsed: 0.060 s
% 7.86/1.79 % (3809177)Peak memory usage: 89 MB
% 7.86/1.79 % (3809177)Instructions burned: 107 (million)
% 7.86/1.79 % (3809180)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=2186672890:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 7.86/1.79 % (3809180)Also succeeded, but the first one will report.
% 7.86/1.79 % (3809150)Refutation found. Thanks to Tanya!
% 7.86/1.79 % SZS status Unsatisfiable for theBenchmark
% 7.86/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 7.86/1.79 % (3809150)------------------------------
% 7.86/1.79 % (3809150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.86/1.79 % (3809150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.86/1.79 % (3809150)CaDiCaL version: 2.1.3
% 7.86/1.79 % (3809150)Termination reason: Refutation
% 7.86/1.79 % (3809150)Time elapsed: 0.628 s
% 7.86/1.79 % (3809150)Peak memory usage: 128 MB
% 7.86/1.79 % (3809150)Instructions burned: 925 (million)
% 7.86/1.79 % (3809150)------------------------------
% 7.86/1.79 % (3809150)------------------------------
% 7.86/1.79 % (3809145)Success in time 1.048 s
% 7.86/1.79 % Vampire exiting
%------------------------------------------------------------------------------