%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL074-3 : 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 : n008.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 09:37:51 AM UTC 2026
% Result : Unsatisfiable 4.13s 1.36s
% Output : Refutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 56 ( 26 unt; 2 def)
% Number of atoms : 87 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 28 ~; 29 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(projection2,pair(X0,X1)) = X1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',pairwise_application) ).
fof(f7,axiom,
! [X0] : apply(eq,pair(X0,X0)) = projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality) ).
fof(f8,plain,
! [X0] : projection1 = apply(eq,pair(X0,X0)),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0,X1] :
( X0 = X1
| apply(eq,pair(X0,X1)) = projection2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
fof(f10,plain,
! [X0,X1] :
( projection2 = apply(eq,pair(X0,X1))
| X0 = X1 ),
inference(reorient_equations,[],[f9]) ).
fof(f12,axiom,
projection1 != projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_projections) ).
fof(f13,axiom,
apply(k,projection1) = k_projection1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_projection1) ).
fof(f14,axiom,
apply(k,projection2) = k_projection2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_projection2) ).
fof(f15,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_referential) ).
fof(f16,plain,
s = apply(eq,pair(apply(k,s),k_projection2)),
inference(forward_demodulation,[],[f15,f14]) ).
fof(f39,plain,
! [X0] : projection1 = apply(k_projection1,X0),
inference(superposition,[],[f1,f13]) ).
fof(f45,plain,
! [X0] : projection2 = apply(k_projection2,X0),
inference(superposition,[],[f1,f14]) ).
fof(f121,plain,
( projection2 = s
| k_projection2 = apply(k,s) ),
inference(superposition,[],[f10,f16]) ).
fof(f126,definition,
( spl0_1
<=> k_projection2 = apply(k,s) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f128,plain,
( k_projection2 = apply(k,s)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f130,definition,
( spl0_2
<=> projection2 = s ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f132,plain,
( projection2 = s
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f134,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f121,f130,f126]) ).
fof(f151,plain,
! [X2,X0,X1] : apply(pair(apply(k,X0),X1),X2) = pair(X0,apply(X1,X2)),
inference(superposition,[],[f5,f1]) ).
fof(f167,plain,
! [X0,X1] : apply(pair(k_projection2,X0),X1) = pair(projection2,apply(X0,X1)),
inference(superposition,[],[f5,f45]) ).
fof(f169,plain,
! [X0] : apply(pair(X0,k),projection2) = pair(apply(X0,projection2),k_projection2),
inference(superposition,[],[f5,f14]) ).
fof(f184,plain,
! [X0] : apply(pair(X0,eq),pair(apply(k,s),k_projection2)) = pair(apply(X0,pair(apply(k,s),k_projection2)),s),
inference(superposition,[],[f5,f16]) ).
fof(f186,plain,
! [X0,X1] : apply(pair(X0,k_projection2),X1) = pair(apply(X0,X1),projection2),
inference(superposition,[],[f5,f45]) ).
fof(f192,plain,
! [X0,X1] : projection1 = apply(eq,apply(pair(X0,X0),X1)),
inference(superposition,[],[f8,f5]) ).
fof(f193,plain,
( ! [X0] : apply(pair(X0,eq),pair(apply(k,projection2),k_projection2)) = pair(apply(X0,pair(apply(k,projection2),k_projection2)),projection2)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f184,f132]) ).
fof(f205,plain,
( ! [X0] : apply(pair(X0,eq),pair(apply(k,projection2),k_projection2)) = apply(pair(X0,k_projection2),pair(apply(k,projection2),k_projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f193,f186]) ).
fof(f207,plain,
( ! [X0] : apply(pair(X0,eq),apply(pair(k,k),projection2)) = apply(pair(X0,k_projection2),apply(pair(k,k),projection2))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f205,f169]) ).
fof(f389,plain,
! [X0] : apply(pair(k_projection2,eq),pair(X0,X0)) = pair(projection2,projection1),
inference(superposition,[],[f167,f8]) ).
fof(f391,plain,
apply(pair(k_projection2,eq),pair(apply(k,s),k_projection2)) = pair(projection2,s),
inference(superposition,[],[f167,f16]) ).
fof(f911,plain,
( ! [X0] : pair(X0,apply(k_projection2,apply(pair(k,k),projection2))) = apply(pair(apply(k,X0),eq),apply(pair(k,k),projection2))
| ~ spl0_2 ),
inference(superposition,[],[f151,f207]) ).
fof(f924,plain,
( ! [X0] : pair(X0,apply(k_projection2,apply(pair(k,k),projection2))) = pair(X0,apply(eq,apply(pair(k,k),projection2)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f911,f151]) ).
fof(f928,plain,
( ! [X0] : pair(X0,projection1) = pair(X0,apply(k_projection2,apply(pair(k,k),projection2)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f924,f192]) ).
fof(f930,plain,
( ! [X0] : pair(X0,projection2) = pair(X0,projection1)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f928,f45]) ).
fof(f937,plain,
( ! [X0] : projection2 = apply(projection2,pair(X0,projection1))
| ~ spl0_2 ),
inference(superposition,[],[f3,f930]) ).
fof(f950,plain,
( projection1 = projection2
| ~ spl0_2 ),
inference(forward_demodulation,[],[f937,f3]) ).
fof(f951,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f950,f12]) ).
fof(f952,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f951]) ).
fof(f956,plain,
( pair(projection2,s) = apply(pair(k_projection2,eq),pair(k_projection2,k_projection2))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f391,f128]) ).
fof(f959,plain,
( pair(projection2,projection1) = pair(projection2,s)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f956,f389]) ).
fof(f1014,plain,
( s = apply(projection2,pair(projection2,projection1))
| ~ spl0_1 ),
inference(superposition,[],[f3,f959]) ).
fof(f1025,plain,
( projection1 = s
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1014,f3]) ).
fof(f1127,plain,
( projection1 = apply(eq,pair(apply(k,projection1),k_projection2))
| ~ spl0_1 ),
inference(superposition,[],[f16,f1025]) ).
fof(f1128,plain,
( projection1 = apply(eq,pair(k_projection1,k_projection2))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1127,f13]) ).
fof(f2006,plain,
( projection1 = projection2
| k_projection1 = k_projection2
| ~ spl0_1 ),
inference(superposition,[],[f10,f1128]) ).
fof(f2020,plain,
( k_projection1 = k_projection2
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f2006,f12]) ).
fof(f2027,plain,
( ! [X0] : projection2 = apply(k_projection1,X0)
| ~ spl0_1 ),
inference(superposition,[],[f45,f2020]) ).
fof(f2046,plain,
( projection1 = projection2
| ~ spl0_1 ),
inference(forward_demodulation,[],[f2027,f39]) ).
fof(f2051,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f2046,f12]) ).
fof(f2052,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f2051]) ).
cnf(s2,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f134]) ).
cnf(s3,plain,
~ spl0_2,
inference(sat_conversion,[],[f952]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f2052]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s3,s4]) ).
fof(f2056,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL074-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:34:35 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.24 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
% 4.13/1.36 % (2677809)Input is clausal, will run a generic CNF schedule.
% 4.13/1.36 % (2677815)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=884340971:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.13/1.36 % (2677819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1223121122:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.13/1.36 % (2677820)dis-21_1_sil=8000:lcm=predicate:random_seed=2290278188: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)
% 4.13/1.36 % (2677818)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1906591647:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.13/1.36 % (2677814)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=576025196:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.13/1.36 % (2677816)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3982098675:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.13/1.36 % (2677817)lrs+10_1_sil=8000:sp=occurrence:random_seed=4147339384:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.13/1.36 % (2677820)Refutation not found, incomplete strategy
% 4.13/1.36 % (2677820)------------------------------
% 4.13/1.36 % (2677820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.36 % (2677820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.36 % (2677820)CaDiCaL version: 2.1.3
% 4.13/1.36 % (2677820)Termination reason: Refutation not found, incomplete strategy
% 4.13/1.36 % (2677820)Time elapsed: 0.001 s
% 4.13/1.36 % (2677820)Peak memory usage: 88 MB
% 4.13/1.36 % (2677817)First to succeed.
% 4.13/1.36 % (2677817)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2677809"
% 4.13/1.36 % (2677818)Instruction limit reached!
% 4.13/1.36 % (2677818)------------------------------
% 4.13/1.36 % (2677818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.36 % (2677818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.36 % (2677818)CaDiCaL version: 2.1.3
% 4.13/1.36 % (2677818)Termination reason: Instruction limit
% 4.13/1.36 % (2677818)Termination phase: Saturation
% 4.13/1.36 % (2677818)Time elapsed: 0.071 s
% 4.13/1.36 % (2677818)Peak memory usage: 89 MB
% 4.13/1.36 % (2677818)Instructions burned: 114 (million)
% 4.13/1.36 % (2677819)Instruction limit reached!
% 4.13/1.36 % (2677819)------------------------------
% 4.13/1.36 % (2677819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.36 % (2677819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.36 % (2677819)CaDiCaL version: 2.1.3
% 4.13/1.36 % (2677819)Termination reason: Instruction limit
% 4.13/1.36 % (2677819)Termination phase: Saturation
% 4.13/1.36 % (2677819)Time elapsed: 0.102 s
% 4.13/1.36 % (2677819)Peak memory usage: 90 MB
% 4.13/1.36 % (2677819)Instructions burned: 182 (million)
% 4.13/1.36 % (2677820)------------------------------
% 4.13/1.36 % (2677820)------------------------------
% 4.13/1.36 % (2677828)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=2796080561:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.13/1.36 % (2677829)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2835984252: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)
% 4.13/1.36 % (2677828)Also succeeded, but the first one will report.
% 4.13/1.36 % (2677817)Refutation found. Thanks to Tanya!
% 4.13/1.36 % SZS status Unsatisfiable for theBenchmark
% 4.13/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 4.13/1.36 % (2677817)------------------------------
% 4.13/1.36 % (2677817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.36 % (2677817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.36 % (2677817)CaDiCaL version: 2.1.3
% 4.13/1.36 % (2677817)Termination reason: Refutation
% 4.13/1.36 % (2677817)Time elapsed: 0.065 s
% 4.13/1.36 % (2677817)Peak memory usage: 91 MB
% 4.13/1.36 % (2677817)Instructions burned: 107 (million)
% 4.13/1.36 % (2677817)------------------------------
% 4.13/1.36 % (2677817)------------------------------
% 4.13/1.36 % (2677809)Success in time 0.493 s
% 4.13/1.36 % Vampire exiting
%------------------------------------------------------------------------------