%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:37:53 AM UTC 2026
% Result : Unsatisfiable 7.88s 1.89s
% Output : Refutation 7.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 11 ( 10 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 7 ~; 1 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f11,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f14,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC2c) ).
fof(f18,plain,
apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))) != apply(k(k(b)),n(apply(abstraction,k(k(b))),k(k(b)))),
inference(unit_resulting_resolution,[],[f11,f14]) ).
fof(f21,plain,
k(b) != apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),
inference(forward_demodulation,[],[f18,f1]) ).
fof(f23,plain,
apply(apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),n(apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),k(b))) != apply(k(b),n(apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),k(b))),
inference(unit_resulting_resolution,[],[f11,f21]) ).
fof(f25,plain,
b != apply(apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),n(apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),k(b))),
inference(forward_demodulation,[],[f23,f1]) ).
fof(f31,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f6,f1]) ).
fof(f64,plain,
b != apply(k(b),apply(n(apply(abstraction,k(k(b))),k(k(b))),n(apply(apply(abstraction,k(k(b))),n(apply(abstraction,k(k(b))),k(k(b)))),k(b)))),
inference(superposition,[],[f25,f31]) ).
fof(f65,plain,
$false,
inference(forward_subsumption_resolution,[],[f64,f1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL081-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:34:25 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 6.04/1.70 % (231106)Input is clausal, will run a generic CNF schedule.
% 6.04/1.70 % (231115)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3275870566:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.04/1.70 % (231117)dis-21_1_sil=8000:lcm=predicate:random_seed=1808850498: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)
% 6.04/1.70 % (231117)Refutation not found, incomplete strategy
% 6.04/1.70 % (231117)------------------------------
% 6.04/1.70 % (231117)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/1.70 % (231117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.70 % (231117)CaDiCaL version: 2.1.3
% 6.04/1.70 % (231117)Termination reason: Refutation not found, incomplete strategy
% 6.04/1.70 % (231117)Time elapsed: 0.001 s
% 6.04/1.70 % (231117)Peak memory usage: 88 MB
% 6.04/1.70 % (231114)lrs+10_1_sil=8000:sp=occurrence:random_seed=3647508689:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.04/1.70 % (231112)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3287613097:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.04/1.70 % (231111)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=4230620493:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.04/1.70 % (231113)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3070276367:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.04/1.70 % (231115)Instruction limit reached!
% 6.04/1.70 % (231115)------------------------------
% 6.04/1.70 % (231115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/1.70 % (231115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.70 % (231115)CaDiCaL version: 2.1.3
% 6.04/1.70 % (231115)Termination reason: Instruction limit
% 6.04/1.70 % (231115)Termination phase: Saturation
% 6.04/1.70 % (231115)Time elapsed: 0.040 s
% 6.04/1.70 % (231115)Peak memory usage: 89 MB
% 6.04/1.70 % (231115)Instructions burned: 117 (million)
% 6.04/1.70 % (231116)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1167929635:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.04/1.70 % (231114)Instruction limit reached!
% 6.04/1.70 % (231114)------------------------------
% 6.04/1.70 % (231114)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/1.70 % (231114)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.70 % (231114)CaDiCaL version: 2.1.3
% 6.04/1.70 % (231114)Termination reason: Instruction limit
% 6.04/1.70 % (231114)Termination phase: Saturation
% 6.04/1.70 % (231114)Time elapsed: 0.069 s
% 6.04/1.70 % (231114)Peak memory usage: 89 MB
% 6.04/1.70 % (231114)Instructions burned: 107 (million)
% 6.04/1.70 % (231124)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=1767325896:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 6.04/1.70 % (231124)Refutation not found, incomplete strategy
% 6.04/1.70 % (231124)------------------------------
% 6.04/1.70 % (231124)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/1.70 % (231124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.70 % (231124)CaDiCaL version: 2.1.3
% 6.04/1.70 % (231124)Termination reason: Refutation not found, incomplete strategy
% 6.04/1.70 % (231124)Time elapsed: 0.001 s
% 6.04/1.70 % (231124)Peak memory usage: 88 MB
% 6.04/1.70 % (231116)Instruction limit reached!
% 6.04/1.70 % (231116)------------------------------
% 6.04/1.70 % (231116)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/1.70 % (231116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/1.70 % (231116)CaDiCaL version: 2.1.3
% 6.04/1.70 % (231116)Termination reason: Instruction limit
% 6.04/1.70 % (231116)Termination phase: Saturation
% 6.04/1.70 % (231116)Time elapsed: 0.106 s
% 6.04/1.70 % (231116)Peak memory usage: 90 MB
% 6.04/1.70 % (231116)Instructions burned: 180 (million)
% 6.04/1.70 % (231126)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2347267785: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)
% 7.88/1.88 % (231117)------------------------------
% 7.88/1.88 % (231117)------------------------------
% 7.88/1.88 % (231128)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3490607174:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 7.88/1.88 % (231128)Refutation not found, incomplete strategy
% 7.88/1.88 % (231128)------------------------------
% 7.88/1.88 % (231128)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.88 % (231128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.88 % (231128)CaDiCaL version: 2.1.3
% 7.88/1.88 % (231128)Termination reason: Refutation not found, incomplete strategy
% 7.88/1.88 % (231128)Time elapsed: 0.001 s
% 7.88/1.88 % (231128)Peak memory usage: 87 MB
% 7.88/1.88 % (231124)------------------------------
% 7.88/1.88 % (231124)------------------------------
% 7.88/1.88 % (231126)Instruction limit reached!
% 7.88/1.88 % (231126)------------------------------
% 7.88/1.88 % (231126)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.88 % (231126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231126)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231126)Termination reason: Instruction limit
% 7.88/1.89 % (231126)Termination phase: Saturation
% 7.88/1.89 % (231126)Time elapsed: 0.115 s
% 7.88/1.89 % (231126)Peak memory usage: 90 MB
% 7.88/1.89 % (231126)Instructions burned: 191 (million)
% 7.88/1.89 % (231132)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1126930715:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 7.88/1.89 % (231131)lrs+10_64_to=lpo:sil=8000:random_seed=872288414:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 7.88/1.89 % (231132)Instruction limit reached!
% 7.88/1.89 % (231132)------------------------------
% 7.88/1.89 % (231132)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231132)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231132)Termination reason: Instruction limit
% 7.88/1.89 % (231132)Termination phase: Saturation
% 7.88/1.89 % (231132)Time elapsed: 0.065 s
% 7.88/1.89 % (231132)Peak memory usage: 90 MB
% 7.88/1.89 % (231132)Instructions burned: 196 (million)
% 7.88/1.89 % (231131)Instruction limit reached!
% 7.88/1.89 % (231131)------------------------------
% 7.88/1.89 % (231131)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231131)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231131)Termination reason: Instruction limit
% 7.88/1.89 % (231131)Termination phase: Saturation
% 7.88/1.89 % (231131)Time elapsed: 0.081 s
% 7.88/1.89 % (231131)Peak memory usage: 89 MB
% 7.88/1.89 % (231131)Instructions burned: 128 (million)
% 7.88/1.89 % (231133)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=3091541191:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 7.88/1.89 % (231128)------------------------------
% 7.88/1.89 % (231128)------------------------------
% 7.88/1.89 % (231136)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1243338789:i=3394:sd=4:ss=included:sgt=64_2994 on theBenchmark for (2994ds/3394Mi)
% 7.88/1.89 % (231133)Instruction limit reached!
% 7.88/1.89 % (231133)------------------------------
% 7.88/1.89 % (231133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231133)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231133)Termination reason: Instruction limit
% 7.88/1.89 % (231133)Termination phase: Saturation
% 7.88/1.89 % (231133)Time elapsed: 0.102 s
% 7.88/1.89 % (231133)Peak memory usage: 91 MB
% 7.88/1.89 % (231133)Instructions burned: 158 (million)
% 7.88/1.89 % (231137)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=1842830868:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2994 on theBenchmark for (2994ds/106Mi)
% 7.88/1.89 % (231112)First to succeed.
% 7.88/1.89 % (231112)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-231106"
% 7.88/1.89 % (231111)Also succeeded, but the first one will report.
% 7.88/1.89 % (231137)Instruction limit reached!
% 7.88/1.89 % (231137)------------------------------
% 7.88/1.89 % (231137)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231137)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231137)Termination reason: Instruction limit
% 7.88/1.89 % (231137)Termination phase: Saturation
% 7.88/1.89 % (231137)Time elapsed: 0.051 s
% 7.88/1.89 % (231137)Peak memory usage: 89 MB
% 7.88/1.89 % (231137)Instructions burned: 108 (million)
% 7.88/1.89 % (231140)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=173350213:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 7.88/1.89 % (231140)Refutation not found, incomplete strategy
% 7.88/1.89 % (231140)------------------------------
% 7.88/1.89 % (231140)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231140)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231140)Termination reason: Refutation not found, incomplete strategy
% 7.88/1.89 % (231140)Time elapsed: 0.001 s
% 7.88/1.89 % (231140)Peak memory usage: 87 MB
% 7.88/1.89 % (231113)Also succeeded, but the first one will report.
% 7.88/1.89 % (231141)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=2453820732:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 7.88/1.89 % (231144)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3795633216:cond=fast:i=5208:av=off_2992 on theBenchmark for (2992ds/5208Mi)
% 7.88/1.89 % (231141)Instruction limit reached!
% 7.88/1.89 % (231141)------------------------------
% 7.88/1.89 % (231141)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231141)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231141)Termination reason: Instruction limit
% 7.88/1.89 % (231141)Termination phase: Saturation
% 7.88/1.89 % (231141)Time elapsed: 0.141 s
% 7.88/1.89 % (231141)Peak memory usage: 91 MB
% 7.88/1.89 % (231141)Instructions burned: 243 (million)
% 7.88/1.89 % (231140)------------------------------
% 7.88/1.89 % (231140)------------------------------
% 7.88/1.89 % (231112)Refutation found. Thanks to Tanya!
% 7.88/1.89 % SZS status Unsatisfiable for theBenchmark
% 7.88/1.89 % SZS output start Proof for theBenchmark
% See solution above
% 7.88/1.89 % (231112)------------------------------
% 7.88/1.89 % (231112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.88/1.89 % (231112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.88/1.89 % (231112)CaDiCaL version: 2.1.3
% 7.88/1.89 % (231112)Termination reason: Refutation
% 7.88/1.89 % (231112)Time elapsed: 0.622 s
% 7.88/1.89 % (231112)Peak memory usage: 127 MB
% 7.88/1.89 % (231112)Instructions burned: 922 (million)
% 7.88/1.89 % (231112)------------------------------
% 7.88/1.89 % (231112)------------------------------
% 7.88/1.89 % (231106)Success in time 1.03 s
% 7.88/1.89 % Vampire exiting
%------------------------------------------------------------------------------