%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : COM016+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 09:40:08 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 8 unt; 0 def)
% Number of atoms : 247 ( 8 equ)
% Maximal formula atoms : 13 ( 5 avg)
% Number of connectives : 350 ( 151 ~; 154 |; 37 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 82 ( 74 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X0)
& aRewritingSystem0(X1)
& aElement0(X2) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCRDef) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f17,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f19,axiom,
( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731_02) ).
fof(f20,conjecture,
? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f21,negated_conjecture,
~ ? [X0] :
( aElement0(X0)
& aReductOfIn0(X0,xa,xR)
& sdtmndtasgtdt0(X0,xR,xb) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f28,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) ) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f32]) ).
fof(f48,plain,
! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtasgtdt0(X0,xR,xb) ),
inference(ennf_transformation,[],[f21]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X0,X1)
& sdtmndtplgtdt0(X3,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X0,X1)
& sdtmndtplgtdt0(X4,X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(rectify,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ( ~ aReductOfIn0(X2,X0,X1)
& ! [X3] :
( ~ aElement0(X3)
| ~ aReductOfIn0(X3,X0,X1)
| ~ sdtmndtplgtdt0(X3,X1,X2) ) ) )
& ( aReductOfIn0(X2,X0,X1)
| ( aElement0(sK4(X0,X1,X2))
& aReductOfIn0(sK4(X0,X1,X2),X0,X1)
& sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2) )
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X4,sK4(X0,X1,X2))],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(nnf_transformation,[],[f33]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( X0 != X2
& ~ sdtmndtplgtdt0(X0,X1,X2) ) )
& ( X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(flattening,[],[f59]) ).
fof(f79,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(sK4(X0,X1,X2),X1,X2)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f80,plain,
! [X2,X0,X1] :
( aReductOfIn0(sK4(X0,X1,X2),X0,X1)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f81,plain,
! [X2,X0,X1] :
( aElement0(sK4(X0,X1,X2))
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f58]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f87,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(cnf_transformation,[],[f60]) ).
fof(f123,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f127,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f128,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f133,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f19]) ).
fof(f134,plain,
! [X0] :
( ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f135,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ),
inference(equality_resolution,[],[f87]) ).
fof(f136,plain,
! [X2,X1] :
( sdtmndtasgtdt0(X2,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1) ),
inference(duplicate_literal_removal,[],[f135]) ).
fof(f155,plain,
( ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aReductOfIn0(xb,xa,xR)
| ~ aElement0(xb) ),
inference(resolution,[],[f136,f134]) ).
fof(f156,plain,
( ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(duplicate_literal_removal,[],[f155]) ).
fof(f157,plain,
( ~ aRewritingSystem0(xR)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(forward_subsumption_resolution,[],[f156,f127]) ).
fof(f158,plain,
~ aReductOfIn0(xb,xa,xR),
inference(forward_subsumption_resolution,[],[f157,f123]) ).
fof(f379,plain,
! [X2,X0,X1] :
( aReductOfIn0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X1,X2,X0)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X0)
| sdtmndtasgtdt0(sK4(X1,X2,X0),X2,X0)
| ~ aElement0(sK4(X1,X2,X0))
| ~ aRewritingSystem0(X2)
| ~ aElement0(X0) ),
inference(resolution,[],[f79,f86]) ).
fof(f381,plain,
! [X2,X0,X1] :
( aReductOfIn0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X1,X2,X0)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X0)
| sdtmndtasgtdt0(sK4(X1,X2,X0),X2,X0)
| ~ aElement0(sK4(X1,X2,X0)) ),
inference(duplicate_literal_removal,[],[f379]) ).
fof(f386,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(sK4(X1,X2,X0),X2,X0)
| ~ sdtmndtplgtdt0(X1,X2,X0)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X0)
| aReductOfIn0(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f381,f81]) ).
fof(f957,plain,
! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xb)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| aReductOfIn0(xb,X0,xR)
| ~ aReductOfIn0(sK4(X0,xR,xb),xa,xR)
| ~ aElement0(sK4(X0,xR,xb)) ),
inference(resolution,[],[f386,f134]) ).
fof(f997,plain,
! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xb)
| ~ aElement0(X0)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb)
| aReductOfIn0(xb,X0,xR)
| ~ aReductOfIn0(sK4(X0,xR,xb),xa,xR) ),
inference(forward_subsumption_resolution,[],[f957,f81]) ).
fof(f1006,plain,
! [X0] :
( ~ sdtmndtplgtdt0(X0,xR,xb)
| ~ aElement0(X0)
| ~ aElement0(xb)
| aReductOfIn0(xb,X0,xR)
| ~ aReductOfIn0(sK4(X0,xR,xb),xa,xR) ),
inference(forward_subsumption_resolution,[],[f997,f123]) ).
fof(f1009,plain,
! [X0] :
( ~ aReductOfIn0(sK4(X0,xR,xb),xa,xR)
| ~ aElement0(X0)
| aReductOfIn0(xb,X0,xR)
| ~ sdtmndtplgtdt0(X0,xR,xb) ),
inference(forward_subsumption_resolution,[],[f1006,f127]) ).
fof(f1010,plain,
( ~ aElement0(xa)
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(resolution,[],[f1009,f80]) ).
fof(f1011,plain,
( ~ aElement0(xa)
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(duplicate_literal_removal,[],[f1010]) ).
fof(f1012,plain,
( aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f1011,f128]) ).
fof(f1013,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f1012,f158]) ).
fof(f1014,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xb) ),
inference(forward_subsumption_resolution,[],[f1013,f133]) ).
fof(f1015,plain,
~ aElement0(xb),
inference(forward_subsumption_resolution,[],[f1014,f123]) ).
fof(f1016,plain,
$false,
inference(forward_subsumption_resolution,[],[f1015,f127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM016+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:48:52 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.20/0.28 % (807697)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (807705)dis+10_1_sil=32000:sp=arity:random_seed=108910717:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (807703)% WARNING: option uhcvi not known.
% 0.20/0.28 % (807702)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2968367319_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (807707)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3561313570:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (807704)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2212087057:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (807703)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=635220273:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (807706)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3617934064:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (807708)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3843062657:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (807705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-807697-807705"...
% 0.20/0.28 % TRYING [1]
% 0.20/0.28 % TRYING [2]
% 0.20/0.28 % (807705)...printing done.
% 0.20/0.28 % (807705)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (807705)------------------------------
% 0.20/0.28 % (807705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (807705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (807705)CaDiCaL version: 2.1.3
% 0.20/0.28 % (807705)Termination reason: Refutation
% 0.20/0.28 % (807705)Time elapsed: 0.011 s
% 0.20/0.28 % (807705)Peak memory usage: 12 MB
% 0.20/0.28 % (807705)Instructions burned: 28 (million)
% 0.20/0.28 % (807697)Success in time 0.048 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------