%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL080-1 : 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 : n016.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 0.19s 1.61s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 20 unt; 3 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 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 : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',abstraction) ).
fof(f11,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
fof(f14,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,k(b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_TRC2b) ).
fof(f15,definition,
sF0 = k(b),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f16,plain,
k(b) = sF0,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF1 = apply(abstraction,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f18,plain,
apply(abstraction,sF0) = sF1,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF2 = apply(abstraction,sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f20,plain,
apply(abstraction,sF1) = sF2,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
sF0 != sF2,
inference(definition_folding,[],[f14,f20,f18,f16,f16]) ).
fof(f23,plain,
k(b) != sF2,
inference(backward_demodulation,[],[f21,f16]) ).
fof(f24,plain,
apply(abstraction,k(b)) = sF1,
inference(forward_demodulation,[],[f18,f16]) ).
fof(f28,plain,
! [X0,X1] : apply(apply(k(b),k(X1)),apply(X0,X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f6,f24]) ).
fof(f29,plain,
! [X0,X1] : apply(apply(sF1,k(X1)),apply(X0,X1)) = apply(apply(sF2,X0),X1),
inference(superposition,[],[f6,f20]) ).
fof(f39,plain,
! [X0,X1] : apply(apply(sF1,X0),X1) = apply(b,apply(X0,X1)),
inference(forward_demodulation,[],[f28,f1]) ).
fof(f40,plain,
! [X0,X1] : apply(apply(sF2,X0),X1) = apply(b,apply(k(X1),apply(X0,X1))),
inference(backward_demodulation,[],[f29,f39]) ).
fof(f41,plain,
! [X0,X1] : apply(apply(sF2,X0),X1) = apply(b,X1),
inference(forward_demodulation,[],[f40,f1]) ).
fof(f44,plain,
! [X0,X1] :
( apply(b,n(apply(sF2,X0),X1)) != apply(X1,n(apply(sF2,X0),X1))
| apply(sF2,X0) = X1 ),
inference(superposition,[],[f11,f41]) ).
fof(f50,plain,
! [X0] : b = apply(sF2,X0),
inference(equality_resolution,[],[f44]) ).
fof(f62,plain,
! [X0] :
( b != apply(X0,n(X0,sF2))
| sF2 = X0 ),
inference(superposition,[],[f11,f50]) ).
fof(f65,plain,
! [X0] :
( k(X0) = sF2
| b != X0 ),
inference(superposition,[],[f62,f1]) ).
fof(f108,plain,
! [X0] :
( k(X0) != k(b)
| b != X0 ),
inference(superposition,[],[f23,f65]) ).
fof(f112,plain,
b != b,
inference(equality_resolution,[],[f108]) ).
fof(f113,plain,
$false,
inference(trivial_inequality_removal,[],[f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL080-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n016.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:39:34 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running first-order theorem proving
% 0.06/0.22 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
% 0.19/1.60 % (4054244)Input is clausal, will run a generic CNF schedule.
% 0.19/1.60 % (4054357)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4172827451:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.19/1.60 % (4054355)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=342238236:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.19/1.60 % (4054361)dis-21_1_sil=8000:lcm=predicate:random_seed=2578390023: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)
% 0.19/1.60 % (4054356)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1244852574:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.19/1.60 % (4054359)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=813497682:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.19/1.60 % (4054360)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3655066275:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.19/1.60 % (4054358)lrs+10_1_sil=8000:sp=occurrence:random_seed=3780950685:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.19/1.60 % (4054361)Refutation not found, incomplete strategy
% 0.19/1.60 % (4054361)------------------------------
% 0.19/1.60 % (4054361)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054361)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054361)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.60 % (4054361)Time elapsed: 0.001 s
% 0.19/1.60 % (4054361)Peak memory usage: 88 MB
% 0.19/1.60 % (4054358)Instruction limit reached!
% 0.19/1.60 % (4054358)------------------------------
% 0.19/1.60 % (4054358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054358)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054358)Termination reason: Instruction limit
% 0.19/1.60 % (4054358)Termination phase: Saturation
% 0.19/1.60 % (4054358)Time elapsed: 0.069 s
% 0.19/1.60 % (4054358)Peak memory usage: 89 MB
% 0.19/1.60 % (4054358)Instructions burned: 108 (million)
% 0.19/1.60 % (4054359)Instruction limit reached!
% 0.19/1.60 % (4054359)------------------------------
% 0.19/1.60 % (4054359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054359)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054359)Termination reason: Instruction limit
% 0.19/1.60 % (4054359)Termination phase: Saturation
% 0.19/1.60 % (4054359)Time elapsed: 0.072 s
% 0.19/1.60 % (4054359)Peak memory usage: 88 MB
% 0.19/1.60 % (4054359)Instructions burned: 114 (million)
% 0.19/1.60 % (4054360)Instruction limit reached!
% 0.19/1.60 % (4054360)------------------------------
% 0.19/1.60 % (4054360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054360)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054360)Termination reason: Instruction limit
% 0.19/1.60 % (4054360)Termination phase: Saturation
% 0.19/1.60 % (4054360)Time elapsed: 0.106 s
% 0.19/1.60 % (4054360)Peak memory usage: 90 MB
% 0.19/1.60 % (4054360)Instructions burned: 181 (million)
% 0.19/1.60 % (4054369)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=1514884521:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.19/1.60 % (4054369)Refutation not found, incomplete strategy
% 0.19/1.60 % (4054369)------------------------------
% 0.19/1.60 % (4054369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054369)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054369)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.60 % (4054369)Time elapsed: 0.001 s
% 0.19/1.60 % (4054369)Peak memory usage: 88 MB
% 0.19/1.60 % (4054370)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=653327640: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)
% 0.19/1.60 % (4054361)------------------------------
% 0.19/1.60 % (4054361)------------------------------
% 0.19/1.60 % (4054371)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2933207441:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.19/1.60 % (4054371)Refutation not found, incomplete strategy
% 0.19/1.60 % (4054371)------------------------------
% 0.19/1.60 % (4054371)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054371)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054371)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.60 % (4054371)Time elapsed: 0.001 s
% 0.19/1.60 % (4054371)Peak memory usage: 87 MB
% 0.19/1.60 % (4054370)Instruction limit reached!
% 0.19/1.60 % (4054370)------------------------------
% 0.19/1.60 % (4054370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.60 % (4054370)CaDiCaL version: 2.1.3
% 0.19/1.60 % (4054370)Termination reason: Instruction limit
% 0.19/1.60 % (4054370)Termination phase: Saturation
% 0.19/1.60 % (4054370)Time elapsed: 0.113 s
% 0.19/1.60 % (4054370)Peak memory usage: 90 MB
% 0.19/1.60 % (4054370)Instructions burned: 190 (million)
% 0.19/1.60 % (4054357)First to succeed.
% 0.19/1.60 % (4054357)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4054244"
% 0.19/1.60 % (4054375)lrs+10_64_to=lpo:sil=8000:random_seed=1779714859:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.19/1.60 % (4054369)------------------------------
% 0.19/1.60 % (4054369)------------------------------
% 0.19/1.60 % (4054376)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3765809838:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 0.19/1.60 % (4054375)Instruction limit reached!
% 0.19/1.60 % (4054375)------------------------------
% 0.19/1.60 % (4054375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.60 % (4054375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.61 % (4054375)CaDiCaL version: 2.1.3
% 0.19/1.61 % (4054375)Termination reason: Instruction limit
% 0.19/1.61 % (4054375)Termination phase: Saturation
% 0.19/1.61 % (4054375)Time elapsed: 0.082 s
% 0.19/1.61 % (4054375)Peak memory usage: 89 MB
% 0.19/1.61 % (4054375)Instructions burned: 127 (million)
% 0.19/1.61 % (4054371)------------------------------
% 0.19/1.61 % (4054371)------------------------------
% 0.19/1.61 % (4054376)Instruction limit reached!
% 0.19/1.61 % (4054376)------------------------------
% 0.19/1.61 % (4054376)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.61 % (4054376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.61 % (4054376)CaDiCaL version: 2.1.3
% 0.19/1.61 % (4054376)Termination reason: Instruction limit
% 0.19/1.61 % (4054376)Termination phase: Saturation
% 0.19/1.61 % (4054376)Time elapsed: 0.067 s
% 0.19/1.61 % (4054376)Peak memory usage: 90 MB
% 0.19/1.61 % (4054376)Instructions burned: 195 (million)
% 0.19/1.61 % (4054379)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2990799778:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 0.19/1.61 % (4054382)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2479778437:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 0.19/1.61 % (4054382)Refutation not found, incomplete strategy
% 0.19/1.61 % (4054382)------------------------------
% 0.19/1.61 % (4054382)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.61 % (4054382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.61 % (4054382)CaDiCaL version: 2.1.3
% 0.19/1.61 % (4054382)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.61 % (4054382)Time elapsed: 0.0000 s
% 0.19/1.61 % (4054382)Peak memory usage: 87 MB
% 0.19/1.61 % (4054380)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=585923734:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 0.19/1.61 % (4054357)Refutation found. Thanks to Tanya!
% 0.19/1.61 % SZS status Unsatisfiable for theBenchmark
% 0.19/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.61 % (4054357)------------------------------
% 0.19/1.61 % (4054357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.61 % (4054357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.61 % (4054357)CaDiCaL version: 2.1.3
% 0.19/1.61 % (4054357)Termination reason: Refutation
% 0.19/1.61 % (4054357)Time elapsed: 0.396 s
% 0.19/1.61 % (4054357)Peak memory usage: 128 MB
% 0.19/1.61 % (4054357)Instructions burned: 938 (million)
% 0.19/1.61 % (4054357)------------------------------
% 0.19/1.61 % (4054357)------------------------------
% 0.19/1.61 % (4054244)Success in time 0.763 s
% 0.19/1.61 % Vampire exiting
%------------------------------------------------------------------------------