%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 09:29:47 AM UTC 2026
% Result : Theorem 0.25s 0.41s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 45 unt; 0 def)
% Number of atoms : 97 ( 65 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 58 ( 20 ~; 15 |; 20 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 36 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
( element(X0)
<=> ? [X1] :
( times(X0,X1) = X0
& times(X0,X0) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,conjecture,
! [X0,X1,X2] :
( ( element(X0)
& element(X1)
& X2 = times(X0,X1) )
=> element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(f4,negated_conjecture,
~ ! [X0,X1,X2] :
( ( element(X0)
& element(X1)
& X2 = times(X0,X1) )
=> element(X2) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
? [X0,X1,X2] :
( ~ element(X2)
& element(X0)
& element(X1)
& X2 = times(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1,X2] :
( ~ element(X2)
& element(X0)
& element(X1)
& X2 = times(X0,X1) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ( element(X0)
| ! [X1] :
( times(X0,X1) != X0
| times(X0,X0) != X1 ) )
& ( ? [X1] :
( times(X0,X1) = X0
& times(X0,X0) = X1 )
| ~ element(X0) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ( element(X0)
| ! [X1] :
( times(X0,X1) != X0
| times(X0,X0) != X1 ) )
& ( ? [X2] :
( times(X0,X2) = X0
& times(X0,X0) = X2 )
| ~ element(X0) ) ),
inference(rectify,[],[f7]) ).
fof(f9,plain,
! [X0] :
( ( element(X0)
| ! [X1] :
( times(X0,X1) != X0
| times(X0,X0) != X1 ) )
& ( ( times(X0,sK0(X0)) = X0
& times(X0,X0) = sK0(X0) )
| ~ element(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f8]) ).
fof(f10,plain,
( ~ element(sK3)
& element(sK1)
& element(sK2)
& sK3 = times(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f6]) ).
fof(f11,plain,
! [X2,X0,X1] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0] :
( ~ element(X0)
| times(X0,X0) = sK0(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0] :
( ~ element(X0)
| times(X0,sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( element(X0)
| times(X0,X1) != X0
| times(X0,X0) != X1 ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
sK3 = times(sK1,sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
element(sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
element(sK1),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
~ element(sK3),
inference(cnf_transformation,[],[f10]) ).
fof(f19,plain,
! [X0] :
( times(X0,times(X0,X0)) != X0
| element(X0) ),
inference(equality_resolution,[],[f14]) ).
fof(f26,plain,
times(sK2,sK2) = sK0(sK2),
inference(resolution,[],[f12,f16]) ).
fof(f27,plain,
times(sK1,sK1) = sK0(sK1),
inference(resolution,[],[f12,f17]) ).
fof(f35,plain,
sK2 = times(sK2,sK0(sK2)),
inference(resolution,[],[f13,f16]) ).
fof(f36,plain,
sK1 = times(sK1,sK0(sK1)),
inference(resolution,[],[f13,f17]) ).
fof(f62,plain,
! [X0] : times(sK0(sK2),times(X0,sK2)) = times(sK2,X0),
inference(superposition,[],[f11,f35]) ).
fof(f65,plain,
! [X0] : times(sK1,times(X0,sK1)) = times(sK0(sK1),X0),
inference(superposition,[],[f11,f27]) ).
fof(f66,plain,
! [X0] : times(sK2,times(X0,sK1)) = times(sK3,X0),
inference(superposition,[],[f11,f15]) ).
fof(f67,plain,
! [X0] : times(sK2,times(X0,sK2)) = times(sK0(sK2),X0),
inference(superposition,[],[f11,f26]) ).
fof(f85,plain,
times(sK3,sK1) = times(sK2,sK0(sK1)),
inference(superposition,[],[f66,f27]) ).
fof(f91,plain,
! [X0] : times(sK0(sK1),times(X0,sK2)) = times(times(sK3,sK1),X0),
inference(superposition,[],[f11,f85]) ).
fof(f92,plain,
! [X0] : times(sK0(sK1),times(X0,sK2)) = times(sK1,times(X0,sK3)),
inference(forward_demodulation,[],[f91,f11]) ).
fof(f93,plain,
times(sK2,sK1) = times(sK0(sK2),sK3),
inference(superposition,[],[f62,f15]) ).
fof(f94,plain,
sK0(sK2) = times(sK0(sK2),sK0(sK2)),
inference(superposition,[],[f62,f26]) ).
fof(f100,plain,
! [X0] : times(sK3,times(X0,sK0(sK2))) = times(times(sK2,sK1),X0),
inference(superposition,[],[f11,f93]) ).
fof(f101,plain,
! [X0] : times(sK3,times(X0,sK0(sK2))) = times(sK1,times(X0,sK2)),
inference(forward_demodulation,[],[f100,f11]) ).
fof(f122,plain,
times(sK1,sK0(sK1)) = times(sK0(sK1),sK1),
inference(superposition,[],[f65,f27]) ).
fof(f127,plain,
sK1 = times(sK0(sK1),sK1),
inference(forward_demodulation,[],[f122,f36]) ).
fof(f133,plain,
! [X0] : times(sK1,X0) = times(sK1,times(X0,sK0(sK1))),
inference(superposition,[],[f11,f127]) ).
fof(f139,plain,
times(sK2,sK0(sK2)) = times(sK0(sK2),sK2),
inference(superposition,[],[f67,f26]) ).
fof(f144,plain,
sK2 = times(sK0(sK2),sK2),
inference(forward_demodulation,[],[f139,f35]) ).
fof(f157,plain,
times(sK1,sK2) = times(sK1,times(sK3,sK1)),
inference(superposition,[],[f133,f85]) ).
fof(f163,plain,
times(sK1,sK2) = times(sK0(sK1),sK3),
inference(forward_demodulation,[],[f157,f65]) ).
fof(f165,plain,
sK3 = times(sK0(sK1),sK3),
inference(forward_demodulation,[],[f163,f15]) ).
fof(f223,plain,
times(sK0(sK1),sK3) = times(sK1,times(sK1,sK3)),
inference(superposition,[],[f92,f15]) ).
fof(f233,plain,
sK3 = times(sK1,times(sK1,sK3)),
inference(forward_demodulation,[],[f223,f165]) ).
fof(f238,plain,
! [X0] : times(sK3,X0) = times(times(sK1,sK3),times(X0,sK1)),
inference(superposition,[],[f11,f233]) ).
fof(f239,plain,
! [X0] : times(sK3,X0) = times(sK3,times(times(X0,sK1),sK1)),
inference(forward_demodulation,[],[f238,f11]) ).
fof(f240,plain,
! [X0] : times(sK3,X0) = times(sK3,times(sK1,times(sK1,X0))),
inference(forward_demodulation,[],[f239,f11]) ).
fof(f264,plain,
times(sK3,sK0(sK2)) = times(sK1,times(sK0(sK2),sK2)),
inference(superposition,[],[f101,f94]) ).
fof(f266,plain,
times(sK3,sK2) = times(sK1,times(sK2,sK2)),
inference(superposition,[],[f101,f35]) ).
fof(f271,plain,
times(sK1,sK0(sK2)) = times(sK3,sK2),
inference(forward_demodulation,[],[f266,f26]) ).
fof(f273,plain,
times(sK1,sK2) = times(sK3,sK0(sK2)),
inference(forward_demodulation,[],[f264,f144]) ).
fof(f277,plain,
sK3 = times(sK3,sK0(sK2)),
inference(forward_demodulation,[],[f273,f15]) ).
fof(f281,plain,
times(sK3,sK3) = times(sK1,times(sK3,sK2)),
inference(superposition,[],[f101,f277]) ).
fof(f285,plain,
times(sK3,sK0(sK2)) = times(sK3,times(sK1,times(sK3,sK2))),
inference(superposition,[],[f240,f271]) ).
fof(f288,plain,
sK3 = times(sK3,times(sK1,times(sK3,sK2))),
inference(forward_demodulation,[],[f285,f277]) ).
fof(f300,plain,
sK3 = times(sK3,times(sK3,sK3)),
inference(forward_demodulation,[],[f288,f281]) ).
fof(f301,plain,
( sK3 != sK3
| element(sK3) ),
inference(superposition,[],[f19,f300]) ).
fof(f303,plain,
element(sK3),
inference(trivial_inequality_removal,[],[f301]) ).
fof(f305,plain,
$false,
inference(forward_subsumption_resolution,[],[f303,f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+2 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 % Computer : n013.cluster.edu
% 0.09/0.25 % Model : x86_64 x86_64
% 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.25 % Memory : 8046.5625MB
% 0.09/0.25 % OS : Linux 6.8.0-71-generic
% 0.09/0.25 % CPULimit : 300
% 0.09/0.25 % WCLimit : 300
% 0.09/0.25 % DateTime : Mon Sep 28 19:42:38 UTC 2026
% 0.09/0.26 % CPUTime :
% 0.09/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.31 Running first-order model finding
% 0.09/0.31 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
% 0.25/0.41 % (1486116)Will run a generic schedule for satisfiability detection.
% 0.25/0.41 % (1486127)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1937193496:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.41 % (1486121)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1342902558_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.41 % (1486123)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2999251205:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.41 % (1486126)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=236616434:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.25/0.41 % (1486124)dis+10_1_sil=32000:sp=arity:random_seed=623400338:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.25/0.41 % (1486125)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2377950944:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.25/0.41 % TRYING [1]
% 0.25/0.41 % TRYING [2]
% 0.25/0.41 % TRYING [3]
% 0.25/0.41 % TRYING [4]
% 0.25/0.41 % TRYING [5]
% 0.25/0.41 % (1486122)% WARNING: option uhcvi not known.
% 0.25/0.41 % (1486122)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1755862111:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.25/0.41 % (1486123) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1486116-1486123"...
% 0.25/0.41 % (1486123)...printing done.
% 0.25/0.41 % (1486123)Refutation found. Thanks to Tanya!
% 0.25/0.41 % SZS status Theorem for theBenchmark
% 0.25/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.41 % (1486123)------------------------------
% 0.25/0.41 % (1486123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.41 % (1486123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.41 % (1486123)CaDiCaL version: 2.1.3
% 0.25/0.41 % (1486123)Termination reason: Refutation
% 0.25/0.41 % (1486123)Time elapsed: 0.020 s
% 0.25/0.41 % (1486123)Peak memory usage: 11 MB
% 0.25/0.41 % (1486123)Instructions burned: 16 (million)
% 0.25/0.41 % (1486116)Success in time 0.091 s
% 0.25/0.41 % Vampire exiting
%------------------------------------------------------------------------------