%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL076-1 : 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 : n017.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 09:37:52 AM UTC 2026
% Result : Unsatisfiable 0.33s 3.31s
% Output : Refutation 0.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 16 unt; 0 def)
% Number of atoms : 26 ( 25 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 10 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 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 : 42 ( 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',projection2) ).
fof(f5,axiom,
! [X2,X0,X1] : apply(pair(X0,X1),X2) = pair(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pairwise_application) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(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(f13,axiom,
! [X0,X1] : apply(apply(f,X0),X1) = apply(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonal_combinator) ).
fof(f14,negated_conjecture,
! [X0] : X0 != apply(eq,pair(apply(k,X0),apply(k,projection2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_self_referential) ).
fof(f15,plain,
! [X0] : apply(eq,pair(apply(k,X0),apply(k,projection2))) != X0,
inference(reorient_equations,[],[f14]) ).
fof(f41,plain,
! [X2,X0,X1] : apply(pair(X1,apply(k,X0)),X2) = pair(apply(X1,X2),X0),
inference(superposition,[],[f5,f1]) ).
fof(f43,plain,
! [X0,X1] :
( apply(X1,n(apply(k,X0),X1)) != X0
| apply(k,X0) = X1 ),
inference(superposition,[],[f11,f1]) ).
fof(f44,plain,
! [X0,X1] :
( apply(X1,n(X1,apply(k,X0))) != X0
| apply(k,X0) = X1 ),
inference(superposition,[],[f11,f1]) ).
fof(f45,plain,
! [X2,X0,X1] : apply(X0,apply(X1,X2)) = apply(apply(apply(abstraction,apply(k,X0)),X1),X2),
inference(superposition,[],[f6,f1]) ).
fof(f80,plain,
! [X2,X0,X1] : apply(pair(X1,projection2),pair(X2,X0)) = pair(apply(X1,pair(X2,X0)),X0),
inference(superposition,[],[f5,f3]) ).
fof(f92,plain,
! [X0] : apply(f,X0) = apply(k,apply(X0,X0)),
inference(unit_resulting_resolution,[],[f43,f13]) ).
fof(f160,plain,
! [X2,X0,X1] :
( pair(apply(X0,n(pair(X0,apply(k,X1)),apply(k,X2))),X1) != X2
| apply(k,X2) = pair(X0,apply(k,X1)) ),
inference(superposition,[],[f44,f41]) ).
fof(f263,plain,
! [X2,X0,X1] :
( pair(X0,X1) != X2
| apply(k,X2) = pair(apply(k,X0),apply(k,X1)) ),
inference(superposition,[],[f160,f1]) ).
fof(f282,plain,
! [X0,X1] : pair(apply(k,X0),apply(k,X1)) = apply(k,pair(X0,X1)),
inference(equality_resolution,[],[f263]) ).
fof(f302,plain,
! [X0] : apply(eq,apply(k,pair(X0,projection2))) != X0,
inference(superposition,[],[f15,f282]) ).
fof(f334,plain,
! [X0,X1] : apply(X0,pair(X1,projection2)) != apply(eq,apply(k,apply(pair(X0,projection2),pair(X1,projection2)))),
inference(superposition,[],[f302,f80]) ).
fof(f347,plain,
! [X0] : apply(X0,pair(X0,projection2)) != apply(eq,apply(f,pair(X0,projection2))),
inference(superposition,[],[f334,f92]) ).
fof(f352,plain,
$false,
inference(unit_resulting_resolution,[],[f347,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL076-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.29 % Computer : n017.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Mon Sep 28 21:29:21 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.30/0.35 Running first-order theorem proving
% 0.30/0.35 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
% 10.26/2.92 % (4058618)Input is clausal, will run a generic CNF schedule.
% 10.26/2.92 % (4058625)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2410620260:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 10.26/2.92 % (4058623)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=3247244601:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 10.26/2.92 % (4058627)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2756893338:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 10.26/2.92 % (4058628)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3369762487:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 10.26/2.92 % (4058629)dis-21_1_sil=8000:lcm=predicate:random_seed=2875011299: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)
% 10.26/2.92 % (4058624)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2299838706:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 10.26/2.92 % (4058626)lrs+10_1_sil=8000:sp=occurrence:random_seed=1477778922:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 10.26/2.92 % (4058629)Refutation not found, incomplete strategy
% 10.26/2.92 % (4058629)------------------------------
% 10.26/2.92 % (4058629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.92 % (4058629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.92 % (4058629)CaDiCaL version: 2.1.3
% 10.26/2.92 % (4058629)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.92 % (4058629)Time elapsed: 0.002 s
% 10.26/2.92 % (4058629)Peak memory usage: 88 MB
% 10.26/2.92 % (4058629)Instructions burned: 1 (million)
% 10.26/2.92 % (4058627)Instruction limit reached!
% 10.26/2.92 % (4058627)------------------------------
% 10.26/2.92 % (4058627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.92 % (4058627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.92 % (4058627)CaDiCaL version: 2.1.3
% 10.26/2.92 % (4058627)Termination reason: Instruction limit
% 10.26/2.92 % (4058627)Termination phase: Saturation
% 10.26/2.92 % (4058627)Time elapsed: 0.107 s
% 10.26/2.92 % (4058627)Peak memory usage: 88 MB
% 10.26/2.92 % (4058627)Instructions burned: 114 (million)
% 10.26/2.92 % (4058626)Instruction limit reached!
% 10.26/2.92 % (4058626)------------------------------
% 10.26/2.92 % (4058626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.92 % (4058626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.92 % (4058626)CaDiCaL version: 2.1.3
% 10.26/2.92 % (4058626)Termination reason: Instruction limit
% 10.26/2.92 % (4058626)Termination phase: Saturation
% 10.26/2.92 % (4058626)Time elapsed: 0.108 s
% 10.26/2.92 % (4058626)Peak memory usage: 89 MB
% 10.26/2.92 % (4058626)Instructions burned: 107 (million)
% 10.26/2.92 % (4058628)Instruction limit reached!
% 10.26/2.92 % (4058628)------------------------------
% 10.26/2.92 % (4058628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.92 % (4058628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.92 % (4058628)CaDiCaL version: 2.1.3
% 10.26/2.92 % (4058628)Termination reason: Instruction limit
% 10.26/2.92 % (4058628)Termination phase: Saturation
% 10.26/2.92 % (4058628)Time elapsed: 0.168 s
% 10.26/2.92 % (4058628)Peak memory usage: 90 MB
% 10.26/2.92 % (4058628)Instructions burned: 180 (million)
% 10.26/2.92 % (4058637)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=2258771323:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 10.26/2.92 % (4058637)Refutation not found, incomplete strategy
% 10.26/2.92 % (4058637)------------------------------
% 10.26/2.92 % (4058637)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.26/2.92 % (4058637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.26/2.92 % (4058637)CaDiCaL version: 2.1.3
% 10.26/2.92 % (4058637)Termination reason: Refutation not found, incomplete strategy
% 10.26/2.92 % (4058637)Time elapsed: 0.003 s
% 10.26/2.92 % (4058637)Peak memory usage: 88 MB
% 10.26/2.92 % (4058637)Instructions burned: 1 (million)
% 10.26/2.92 % (4058629)------------------------------
% 0.33/3.31 % (4058629)------------------------------
% 0.33/3.31 % (4058638)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1686742658:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 0.33/3.31 % (4058639)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2408100756:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 0.33/3.31 % (4058638)Instruction limit reached!
% 0.33/3.31 % (4058638)------------------------------
% 0.33/3.31 % (4058638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058638)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058638)Termination reason: Instruction limit
% 0.33/3.31 % (4058638)Termination phase: Saturation
% 0.33/3.31 % (4058638)Time elapsed: 0.191 s
% 0.33/3.31 % (4058638)Peak memory usage: 90 MB
% 0.33/3.31 % (4058638)Instructions burned: 190 (million)
% 0.33/3.31 % (4058639)Instruction limit reached!
% 0.33/3.31 % (4058639)------------------------------
% 0.33/3.31 % (4058639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058639)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058639)Termination reason: Instruction limit
% 0.33/3.31 % (4058639)Termination phase: Saturation
% 0.33/3.31 % (4058639)Time elapsed: 0.200 s
% 0.33/3.31 % (4058639)Peak memory usage: 89 MB
% 0.33/3.31 % (4058639)Instructions burned: 219 (million)
% 0.33/3.31 % (4058642)lrs+10_64_to=lpo:sil=8000:random_seed=2248158371:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 0.33/3.31 % (4058637)------------------------------
% 0.33/3.31 % (4058637)------------------------------
% 0.33/3.31 % (4058642)Instruction limit reached!
% 0.33/3.31 % (4058642)------------------------------
% 0.33/3.31 % (4058642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058642)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058642)Termination reason: Instruction limit
% 0.33/3.31 % (4058642)Termination phase: Saturation
% 0.33/3.31 % (4058642)Time elapsed: 0.133 s
% 0.33/3.31 % (4058642)Peak memory usage: 89 MB
% 0.33/3.31 % (4058642)Instructions burned: 126 (million)
% 0.33/3.31 % (4058644)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2939603790:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 0.33/3.31 % (4058645)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2259910567:i=157:gtg=all_2990 on theBenchmark for (2990ds/157Mi)
% 0.33/3.31 % (4058647)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=687441128:i=3394:sd=4:ss=included:sgt=64_2989 on theBenchmark for (2989ds/3394Mi)
% 0.33/3.31 % (4058644)Instruction limit reached!
% 0.33/3.31 % (4058644)------------------------------
% 0.33/3.31 % (4058644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058644)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058644)Termination reason: Instruction limit
% 0.33/3.31 % (4058644)Termination phase: Saturation
% 0.33/3.31 % (4058644)Time elapsed: 0.192 s
% 0.33/3.31 % (4058644)Peak memory usage: 89 MB
% 0.33/3.31 % (4058644)Instructions burned: 194 (million)
% 0.33/3.31 % (4058624)First to succeed.
% 0.33/3.31 % (4058645)Instruction limit reached!
% 0.33/3.31 % (4058645)------------------------------
% 0.33/3.31 % (4058645)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058645)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058645)Termination reason: Instruction limit
% 0.33/3.31 % (4058645)Termination phase: Saturation
% 0.33/3.31 % (4058645)Time elapsed: 0.170 s
% 0.33/3.31 % (4058645)Peak memory usage: 91 MB
% 0.33/3.31 % (4058645)Instructions burned: 157 (million)
% 0.33/3.31 % (4058648)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=1525123575:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2988 on theBenchmark for (2988ds/106Mi)
% 0.33/3.31 % (4058624)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4058618"
% 0.33/3.31 % (4058648)Instruction limit reached!
% 0.33/3.31 % (4058648)------------------------------
% 0.33/3.31 % (4058648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058648)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058648)Termination reason: Instruction limit
% 0.33/3.31 % (4058648)Termination phase: Saturation
% 0.33/3.31 % (4058648)Time elapsed: 0.091 s
% 0.33/3.31 % (4058648)Peak memory usage: 89 MB
% 0.33/3.31 % (4058648)Instructions burned: 107 (million)
% 0.33/3.31 % (4058652)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2974631581:i=107_2986 on theBenchmark for (2986ds/107Mi)
% 0.33/3.31 % (4058654)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1375911452:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2986 on theBenchmark for (2986ds/242Mi)
% 0.33/3.31 % (4058652)Instruction limit reached!
% 0.33/3.31 % (4058652)------------------------------
% 0.33/3.31 % (4058652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058652)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058652)Termination reason: Instruction limit
% 0.33/3.31 % (4058652)Termination phase: Saturation
% 0.33/3.31 % (4058652)Time elapsed: 0.113 s
% 0.33/3.31 % (4058652)Peak memory usage: 88 MB
% 0.33/3.31 % (4058652)Instructions burned: 107 (million)
% 0.33/3.31 % (4058655)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=1580790773:cond=fast:i=5208:av=off_2985 on theBenchmark for (2985ds/5208Mi)
% 0.33/3.31 % (4058624)Refutation found. Thanks to Tanya!
% 0.33/3.31 % SZS status Unsatisfiable for theBenchmark
% 0.33/3.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.33/3.31 % (4058624)------------------------------
% 0.33/3.31 % (4058624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.33/3.31 % (4058624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/3.31 % (4058624)CaDiCaL version: 2.1.3
% 0.33/3.31 % (4058624)Termination reason: Refutation
% 0.33/3.31 % (4058624)Time elapsed: 1.111 s
% 0.33/3.31 % (4058624)Peak memory usage: 129 MB
% 0.33/3.31 % (4058624)Instructions burned: 1032 (million)
% 0.33/3.31 % (4058624)------------------------------
% 0.33/3.31 % (4058624)------------------------------
% 0.33/3.31 % (4058618)Success in time 1.817 s
% 0.33/3.31 % Vampire exiting
%------------------------------------------------------------------------------