%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COL078-2 : 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 : n018.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 09:38:24 AM UTC 2026
% Result : Unsatisfiable 1.55s 0.91s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 7 ( 2 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 : 35 ( 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0] : apply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
fof(f5,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1b) ).
fof(f12,plain,
! [X0] :
( n(identity,X0) != apply(X0,n(identity,X0))
| identity = X0 ),
inference(superposition,[],[f3,f4]) ).
fof(f15,plain,
! [X0,X1] :
( apply(X1,n(X1,k(X0))) != X0
| k(X0) = X1 ),
inference(superposition,[],[f3,f1]) ).
fof(f113,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f299,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,X1),X2)) = apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2),
inference(superposition,[],[f113,f2]) ).
fof(f306,plain,
! [X2,X0,X1] :
( apply(X0,apply(X1,n(apply(apply(abstraction,k(X0)),X1),k(X2)))) != X2
| k(X2) = apply(apply(abstraction,k(X0)),X1) ),
inference(superposition,[],[f15,f113]) ).
fof(f976,plain,
! [X2,X0,X1] : apply(k(X0),apply(apply(X1,k(X0)),apply(X2,X0))) = apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X0),
inference(superposition,[],[f2,f299]) ).
fof(f984,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X0) = X0,
inference(forward_demodulation,[],[f976,f1]) ).
fof(f1093,plain,
! [X0,X1] :
( n(identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1)) != n(identity,apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1))
| identity = apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1) ),
inference(superposition,[],[f12,f984]) ).
fof(f1095,plain,
! [X0,X1] : identity = apply(apply(abstraction,apply(apply(abstraction,abstraction),X0)),X1),
inference(trivial_inequality_removal,[],[f1093]) ).
fof(f1126,plain,
! [X0,X1] :
( identity != X1
| k(X1) = apply(abstraction,apply(apply(abstraction,abstraction),X0)) ),
inference(superposition,[],[f15,f1095]) ).
fof(f1307,plain,
! [X0] : k(identity) = apply(abstraction,apply(apply(abstraction,abstraction),X0)),
inference(equality_resolution,[],[f1126]) ).
fof(f3894,plain,
! [X0] :
( k(identity) != X0
| k(X0) = apply(apply(abstraction,k(abstraction)),apply(abstraction,abstraction)) ),
inference(superposition,[],[f306,f1307]) ).
fof(f3896,plain,
! [X0] :
( k(identity) != X0
| k(X0) = apply(apply(apply(abstraction,abstraction),abstraction),abstraction) ),
inference(forward_demodulation,[],[f3894,f2]) ).
fof(f4059,plain,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) = k(k(identity)),
inference(equality_resolution,[],[f3896]) ).
fof(f4060,plain,
$false,
inference(forward_subsumption_resolution,[],[f4059,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.26 % Computer : n018.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Mon Sep 28 21:36:25 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 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
% 1.55/0.91 % (3814981)Will run a generic schedule for satisfiability detection.
% 1.55/0.91 % (3814988)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2839041909:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 1.55/0.91 % (3814987)% WARNING: option uhcvi not known.
% 1.55/0.91 % (3814989)dis+10_1_sil=32000:sp=arity:random_seed=3323347214:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 1.55/0.91 % (3814992)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2637787621:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 1.55/0.91 % (3814990)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2736297889:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 1.55/0.91 % (3814986)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=333250787_3000 on theBenchmark for (3000ds/0Mi)
% 1.55/0.91 % (3814987)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4060059487:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 1.55/0.91 % (3814991)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3411374356:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 1.55/0.91 % TRYING [1]
% 1.55/0.91 % TRYING [2]
% 1.55/0.91 % TRYING [3]
% 1.55/0.91 % TRYING [4]
% 1.55/0.91 % TRYING [5]
% 1.55/0.91 % TRYING [6]
% 1.55/0.91 % (3814989)Instruction limit reached!
% 1.55/0.91 % (3814989)------------------------------
% 1.55/0.91 % (3814989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3814989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3814989)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3814989)Termination reason: Instruction limit
% 1.55/0.91 % (3814989)Termination phase: Saturation
% 1.55/0.91 % (3814989)Time elapsed: 0.098 s
% 1.55/0.91 % (3814989)Peak memory usage: 12 MB
% 1.55/0.91 % (3814989)Instructions burned: 103 (million)
% 1.55/0.91 % (3814990)Instruction limit reached!
% 1.55/0.91 % (3814990)------------------------------
% 1.55/0.91 % (3814990)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3814990)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3814990)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3814990)Termination reason: Instruction limit
% 1.55/0.91 % (3814990)Termination phase: Saturation
% 1.55/0.91 % (3814990)Time elapsed: 0.117 s
% 1.55/0.91 % (3814990)Peak memory usage: 12 MB
% 1.55/0.91 % (3814990)Instructions burned: 116 (million)
% 1.55/0.91 % (3814991)Instruction limit reached!
% 1.55/0.91 % (3814991)------------------------------
% 1.55/0.91 % (3814991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3814991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3814991)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3814991)Termination reason: Instruction limit
% 1.55/0.91 % (3814991)Termination phase: Saturation
% 1.55/0.91 % (3814991)Time elapsed: 0.130 s
% 1.55/0.91 % (3814991)Peak memory usage: 13 MB
% 1.55/0.91 % (3814991)Instructions burned: 131 (million)
% 1.55/0.91 % (3815000)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3251656000:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 1.55/0.91 % TRYING [1]
% 1.55/0.91 % TRYING [2]
% 1.55/0.91 % TRYING [3]
% 1.55/0.91 % TRYING [4]
% 1.55/0.91 % TRYING [7]
% 1.55/0.91 % (3815001)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2458827442:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 1.55/0.91 % TRYING [5]
% 1.55/0.91 % (3814992)Instruction limit reached!
% 1.55/0.91 % (3814992)------------------------------
% 1.55/0.91 % (3814992)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3814992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3814992)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3814992)Termination reason: Instruction limit
% 1.55/0.91 % (3814992)Termination phase: Saturation
% 1.55/0.91 % (3814992)Time elapsed: 0.162 s
% 1.55/0.91 % (3814992)Peak memory usage: 12 MB
% 1.55/0.91 % (3814992)Instructions burned: 159 (million)
% 1.55/0.91 % (3815002)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=1533374052:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 1.55/0.91 % (3815005)ott-21_1_sil=16000:fs=off:random_seed=2447700179:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.55/0.91 % TRYING [6]
% 1.55/0.91 % (3815001)Instruction limit reached!
% 1.55/0.91 % (3815001)------------------------------
% 1.55/0.91 % (3815001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3815001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3815001)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3815001)Termination reason: Instruction limit
% 1.55/0.91 % (3815001)Termination phase: Saturation
% 1.55/0.91 % (3815001)Time elapsed: 0.141 s
% 1.55/0.91 % (3815001)Peak memory usage: 13 MB
% 1.55/0.91 % (3815001)Instructions burned: 131 (million)
% 1.55/0.91 % TRYING [7]
% 1.55/0.91 % (3815008)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2904652188:i=477:bd=all_2996 on theBenchmark for (2996ds/477Mi)
% 1.55/0.91 % TRYING [8]
% 1.55/0.91 % (3815005)Instruction limit reached!
% 1.55/0.91 % (3815005)------------------------------
% 1.55/0.91 % (3815005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3815005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3815005)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3815005)Termination reason: Instruction limit
% 1.55/0.91 % (3815005)Termination phase: Saturation
% 1.55/0.91 % (3815005)Time elapsed: 0.178 s
% 1.55/0.91 % (3815005)Peak memory usage: 12 MB
% 1.55/0.91 % (3815005)Instructions burned: 181 (million)
% 1.55/0.91 % (3815010)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2596286672:fmbsr=1.3:i=865:ins=25_2996 on theBenchmark for (2996ds/865Mi)
% 1.55/0.91 % TRYING [1]
% 1.55/0.91 % TRYING [2]
% 1.55/0.91 % TRYING [3]
% 1.55/0.91 % TRYING [4]
% 1.55/0.91 % TRYING [5]
% 1.55/0.91 % TRYING [6]
% 1.55/0.91 % (3815008) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3814981-3815008"...
% 1.55/0.91 % TRYING [7]
% 1.55/0.91 % (3815008)...printing done.
% 1.55/0.91 % (3815008)Refutation found. Thanks to Tanya!
% 1.55/0.91 % SZS status Unsatisfiable for theBenchmark
% 1.55/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 1.55/0.91 % (3815008)------------------------------
% 1.55/0.91 % (3815008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.55/0.91 % (3815008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.55/0.91 % (3815008)CaDiCaL version: 2.1.3
% 1.55/0.91 % (3815008)Termination reason: Refutation
% 1.55/0.91 % (3815008)Time elapsed: 0.221 s
% 1.55/0.91 % (3815008)Peak memory usage: 14 MB
% 1.55/0.91 % (3815008)Instructions burned: 235 (million)
% 1.55/0.91 % (3814981)Success in time 0.59 s
% 1.55/0.91 % Vampire exiting
%------------------------------------------------------------------------------