%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 09:38:23 AM UTC 2026
% Result : Unsatisfiable 2.93s 0.68s
% Output : Refutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 44 ( 37 unt; 5 def)
% Number of atoms : 51 ( 50 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 11 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 46 ( 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',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/Axioms/COL001-0.ax',abstraction) ).
fof(f11,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/COL001-0.ax',extensionality2) ).
fof(f13,axiom,
! [X0] : apply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
fof(f14,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1b) ).
fof(f15,definition,
sF0 = apply(abstraction,abstraction),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f16,plain,
apply(abstraction,abstraction) = sF0,
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF1 = apply(sF0,abstraction),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f18,plain,
apply(sF0,abstraction) = sF1,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF2 = apply(sF1,abstraction),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f20,plain,
apply(sF1,abstraction) = sF2,
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
sF3 = k(identity),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f22,plain,
k(identity) = sF3,
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
sF4 = k(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f24,plain,
k(sF3) = sF4,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
sF2 != sF4,
inference(definition_folding,[],[f14,f24,f22,f20,f18,f16]) ).
fof(f26,plain,
! [X0] : identity = apply(sF3,X0),
inference(superposition,[],[f1,f22]) ).
fof(f27,plain,
! [X0] : sF3 = apply(sF4,X0),
inference(superposition,[],[f1,f24]) ).
fof(f41,plain,
! [X0] :
( n(identity,X0) != apply(X0,n(identity,X0))
| identity = X0 ),
inference(superposition,[],[f11,f13]) ).
fof(f42,plain,
! [X0] :
( identity != apply(X0,n(sF3,X0))
| sF3 = X0 ),
inference(superposition,[],[f11,f26]) ).
fof(f49,plain,
! [X0] :
( sF3 != apply(X0,n(X0,sF4))
| sF4 = X0 ),
inference(superposition,[],[f11,f27]) ).
fof(f51,plain,
! [X0,X1] : apply(apply(abstraction,k(X1)),apply(X0,X1)) = apply(apply(sF0,X0),X1),
inference(superposition,[],[f6,f16]) ).
fof(f52,plain,
! [X2,X0,X1] : apply(apply(k(X1),k(X2)),apply(apply(X0,X1),X2)) = apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2),
inference(superposition,[],[f6,f6]) ).
fof(f54,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f6,f1]) ).
fof(f80,plain,
! [X2,X0,X1] : apply(apply(k(X1),k(X2)),apply(apply(X0,X1),X2)) = apply(apply(apply(sF0,X0),X1),X2),
inference(forward_demodulation,[],[f52,f16]) ).
fof(f81,plain,
! [X2,X0,X1] : apply(apply(apply(sF0,X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
inference(forward_demodulation,[],[f80,f1]) ).
fof(f180,plain,
! [X0,X1] : apply(apply(sF0,k(X0)),X1) = apply(apply(abstraction,k(X1)),X0),
inference(superposition,[],[f51,f1]) ).
fof(f189,plain,
apply(apply(sF0,abstraction),abstraction) = apply(apply(abstraction,k(abstraction)),sF0),
inference(superposition,[],[f51,f16]) ).
fof(f202,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(sF0,X1)),X2),X0) = apply(apply(apply(abstraction,k(k(X0))),apply(X1,k(X0))),apply(X2,X0)),
inference(superposition,[],[f6,f51]) ).
fof(f204,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(sF0,X1)),X2),X0) = apply(k(X0),apply(apply(X1,k(X0)),apply(X2,X0))),
inference(forward_demodulation,[],[f202,f54]) ).
fof(f206,plain,
apply(sF1,abstraction) = apply(apply(abstraction,k(abstraction)),sF0),
inference(forward_demodulation,[],[f189,f18]) ).
fof(f208,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(sF0,X1)),X2),X0) = X0,
inference(forward_demodulation,[],[f204,f1]) ).
fof(f209,plain,
apply(sF1,abstraction) = apply(apply(sF0,k(sF0)),abstraction),
inference(forward_demodulation,[],[f206,f180]) ).
fof(f210,plain,
sF2 = apply(apply(sF0,k(sF0)),abstraction),
inference(forward_demodulation,[],[f209,f20]) ).
fof(f897,plain,
! [X0] : apply(abstraction,apply(apply(k(sF0),abstraction),X0)) = apply(sF2,X0),
inference(superposition,[],[f81,f210]) ).
fof(f900,plain,
! [X0] : apply(abstraction,apply(sF0,X0)) = apply(sF2,X0),
inference(forward_demodulation,[],[f897,f1]) ).
fof(f3330,plain,
( sF3 != apply(abstraction,apply(sF0,n(sF2,sF4)))
| sF2 = sF4 ),
inference(superposition,[],[f49,f900]) ).
fof(f3332,plain,
sF3 != apply(abstraction,apply(sF0,n(sF2,sF4))),
inference(forward_subsumption_resolution,[],[f3330,f25]) ).
fof(f3699,plain,
! [X0,X1] :
( n(identity,apply(apply(abstraction,apply(sF0,X0)),X1)) != n(identity,apply(apply(abstraction,apply(sF0,X0)),X1))
| identity = apply(apply(abstraction,apply(sF0,X0)),X1) ),
inference(superposition,[],[f41,f208]) ).
fof(f3728,plain,
! [X0,X1] : identity = apply(apply(abstraction,apply(sF0,X0)),X1),
inference(trivial_inequality_removal,[],[f3699]) ).
fof(f11095,plain,
! [X0] :
( identity != identity
| sF3 = apply(abstraction,apply(sF0,X0)) ),
inference(superposition,[],[f42,f3728]) ).
fof(f11097,plain,
! [X0] : sF3 = apply(abstraction,apply(sF0,X0)),
inference(trivial_inequality_removal,[],[f11095]) ).
fof(f11359,plain,
sF3 != sF3,
inference(superposition,[],[f3332,f11097]) ).
fof(f11388,plain,
$false,
inference(trivial_inequality_removal,[],[f11359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL078-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:39:04 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.93/0.67 % (4052619)Will run a generic schedule for satisfiability detection.
% 2.93/0.67 % (4052630)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1877655021:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.93/0.67 % (4052625)% WARNING: option uhcvi not known.
% 2.93/0.67 % (4052624)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=580555066_2999 on theBenchmark for (2999ds/0Mi)
% 2.93/0.67 % (4052626)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4044890901:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.93/0.67 % (4052627)dis+10_1_sil=32000:sp=arity:random_seed=1640094481:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.93/0.67 % (4052628)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3173541600:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.93/0.67 % (4052625)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1762553703:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.93/0.67 % (4052629)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=556564831:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.93/0.67 % TRYING [1]
% 2.93/0.67 % TRYING [2]
% 2.93/0.67 % TRYING [3]
% 2.93/0.67 % TRYING [4]
% 2.93/0.67 % TRYING [5]
% 2.93/0.67 % (4052630)Instruction limit reached!
% 2.93/0.67 % (4052630)------------------------------
% 2.93/0.67 % (4052630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.67 % (4052630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.67 % (4052630)CaDiCaL version: 2.1.3
% 2.93/0.67 % (4052630)Termination reason: Instruction limit
% 2.93/0.67 % (4052630)Termination phase: Saturation
% 2.93/0.67 % (4052630)Time elapsed: 0.056 s
% 2.93/0.67 % (4052630)Peak memory usage: 13 MB
% 2.93/0.67 % (4052630)Instructions burned: 159 (million)
% 2.93/0.67 % TRYING [6]
% 2.93/0.67 % (4052627)Instruction limit reached!
% 2.93/0.67 % (4052627)------------------------------
% 2.93/0.67 % (4052627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.67 % (4052627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.67 % (4052627)CaDiCaL version: 2.1.3
% 2.93/0.67 % (4052627)Termination reason: Instruction limit
% 2.93/0.67 % (4052627)Termination phase: Saturation
% 2.93/0.67 % (4052627)Time elapsed: 0.059 s
% 2.93/0.67 % (4052627)Peak memory usage: 12 MB
% 2.93/0.67 % (4052627)Instructions burned: 103 (million)
% 2.93/0.67 % (4052638)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=702300304:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.93/0.67 % TRYING [1]
% 2.93/0.67 % TRYING [2]
% 2.93/0.67 % TRYING [3]
% 2.93/0.67 % TRYING [4]
% 2.93/0.67 % TRYING [5]
% 2.93/0.67 % (4052628)Instruction limit reached!
% 2.93/0.67 % (4052628)------------------------------
% 2.93/0.67 % (4052628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.67 % (4052628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.67 % (4052628)CaDiCaL version: 2.1.3
% 2.93/0.67 % (4052628)Termination reason: Instruction limit
% 2.93/0.67 % (4052628)Termination phase: Saturation
% 2.93/0.67 % (4052628)Time elapsed: 0.071 s
% 2.93/0.67 % (4052628)Peak memory usage: 12 MB
% 2.93/0.67 % (4052628)Instructions burned: 116 (million)
% 2.93/0.67 % (4052629)Instruction limit reached!
% 2.93/0.67 % (4052629)------------------------------
% 2.93/0.67 % (4052629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.67 % (4052629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.67 % (4052629)CaDiCaL version: 2.1.3
% 2.93/0.67 % (4052629)Termination reason: Instruction limit
% 2.93/0.67 % (4052629)Termination phase: Saturation
% 2.93/0.67 % (4052629)Time elapsed: 0.078 s
% 2.93/0.67 % (4052629)Peak memory usage: 13 MB
% 2.93/0.67 % (4052629)Instructions burned: 131 (million)
% 2.93/0.67 % (4052639)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2645382268:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.93/0.67 % TRYING [6]
% 2.93/0.67 % (4052641)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4244371216:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.93/0.67 % (4052643)ott-21_1_sil=16000:fs=off:random_seed=855548378:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.93/0.67 % TRYING [7]
% 2.93/0.67 % TRYING [7]
% 2.93/0.67 % (4052639)Instruction limit reached!
% 2.93/0.67 % (4052639)------------------------------
% 2.93/0.67 % (4052639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.68 % (4052639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.68 % (4052639)CaDiCaL version: 2.1.3
% 2.93/0.68 % (4052639)Termination reason: Instruction limit
% 2.93/0.68 % (4052639)Termination phase: Saturation
% 2.93/0.68 % (4052639)Time elapsed: 0.081 s
% 2.93/0.68 % (4052639)Peak memory usage: 12 MB
% 2.93/0.68 % (4052639)Instructions burned: 133 (million)
% 2.93/0.68 % (4052646)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4071013252:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.93/0.68 % (4052643)Instruction limit reached!
% 2.93/0.68 % (4052643)------------------------------
% 2.93/0.68 % (4052643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.68 % (4052643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.68 % (4052643)CaDiCaL version: 2.1.3
% 2.93/0.68 % (4052643)Termination reason: Instruction limit
% 2.93/0.68 % (4052643)Termination phase: Saturation
% 2.93/0.68 % (4052643)Time elapsed: 0.098 s
% 2.93/0.68 % (4052643)Peak memory usage: 12 MB
% 2.93/0.68 % (4052643)Instructions burned: 180 (million)
% 2.93/0.68 % (4052648)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2349566389:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 2.93/0.68 % (4052638)Instruction limit reached!
% 2.93/0.68 % (4052638)------------------------------
% 2.93/0.68 % (4052638)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.68 % (4052638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.68 % (4052638)CaDiCaL version: 2.1.3
% 2.93/0.68 % (4052638)Termination reason: Instruction limit
% 2.93/0.68 % (4052638)Termination phase: Finite model building SAT solving
% 2.93/0.68 % (4052638)Time elapsed: 0.158 s
% 2.93/0.68 % (4052638)Peak memory usage: 34 MB
% 2.93/0.68 % (4052638)Instructions burned: 716 (million)
% 2.93/0.68 % TRYING [1]
% 2.93/0.68 % TRYING [2]
% 2.93/0.68 % TRYING [3]
% 2.93/0.68 % TRYING [4]
% 2.93/0.68 % (4052650)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1170157787:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.93/0.68 % TRYING [5]
% 2.93/0.68 % TRYING [8]
% 2.93/0.68 % TRYING [6]
% 2.93/0.68 % TRYING [7]
% 2.93/0.68 % (4052650) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4052619-4052650"...
% 2.93/0.68 % (4052650)...printing done.
% 2.93/0.68 % (4052650)Refutation found. Thanks to Tanya!
% 2.93/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.93/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.93/0.68 % (4052650)------------------------------
% 2.93/0.68 % (4052650)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.93/0.68 % (4052650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.93/0.68 % (4052650)CaDiCaL version: 2.1.3
% 2.93/0.68 % (4052650)Termination reason: Refutation
% 2.93/0.68 % (4052650)Time elapsed: 0.187 s
% 2.93/0.68 % (4052650)Peak memory usage: 19 MB
% 2.93/0.68 % (4052650)Instructions burned: 585 (million)
% 2.93/0.68 % (4052619)Success in time 0.458 s
% 2.93/0.68 % Vampire exiting
%------------------------------------------------------------------------------