%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG210+1 : 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 : n005.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 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 44 unt; 0 def)
% Number of atoms : 68 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 21 ~; 5 |; 7 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 52 !; 5 ?)
% 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] :
( ( element(X0)
& element(X1) )
=> element(times(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(f4,negated_conjecture,
~ ! [X0,X1] :
( ( element(X0)
& element(X1) )
=> element(times(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
? [X0,X1] :
( ~ element(times(X0,X1))
& element(X0)
& element(X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0,X1] :
( ~ element(times(X0,X1))
& element(X0)
& element(X1) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X2,X0,X1] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
inference(cnf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0] :
( ~ element(X0)
| times(X0,X0) = sK0(X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ~ element(X0)
| times(X0,sK0(X0)) = X0 ),
inference(cnf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( times(X0,X0) != X1
| times(X0,X1) != X0
| element(X0) ),
inference(cnf_transformation,[],[f2]) ).
fof(f11,plain,
element(sK2),
inference(cnf_transformation,[],[f6]) ).
fof(f12,plain,
element(sK1),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
~ element(times(sK1,sK2)),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X0] :
( element(X0)
| times(X0,times(X0,X0)) != X0 ),
inference(equality_resolution,[],[f10]) ).
fof(f15,plain,
sK0(sK2) = times(sK2,sK2),
inference(resolution,[],[f8,f11]) ).
fof(f16,plain,
sK0(sK1) = times(sK1,sK1),
inference(resolution,[],[f8,f12]) ).
fof(f17,plain,
sK2 = times(sK2,sK0(sK2)),
inference(resolution,[],[f9,f11]) ).
fof(f18,plain,
sK1 = times(sK1,sK0(sK1)),
inference(resolution,[],[f9,f12]) ).
fof(f19,plain,
times(sK1,sK2) != times(times(sK1,sK2),times(times(sK1,sK2),times(sK1,sK2))),
inference(resolution,[],[f14,f13]) ).
fof(f22,plain,
times(sK1,sK2) != times(sK2,times(times(times(sK1,sK2),times(sK1,sK2)),sK1)),
inference(forward_demodulation,[],[f19,f7]) ).
fof(f23,plain,
times(sK1,sK2) != times(sK2,times(times(sK1,sK2),times(sK1,times(sK1,sK2)))),
inference(forward_demodulation,[],[f22,f7]) ).
fof(f24,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(times(sK1,times(sK1,sK2)),sK1))),
inference(forward_demodulation,[],[f23,f7]) ).
fof(f25,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(times(sK1,sK2),times(sK1,sK1)))),
inference(forward_demodulation,[],[f24,f7]) ).
fof(f26,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK2,times(times(sK1,sK1),sK1)))),
inference(forward_demodulation,[],[f25,f7]) ).
fof(f27,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK2,times(sK1,times(sK1,sK1))))),
inference(forward_demodulation,[],[f26,f7]) ).
fof(f28,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK2,times(sK1,sK0(sK1))))),
inference(forward_demodulation,[],[f27,f16]) ).
fof(f29,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK2,sK1))),
inference(forward_demodulation,[],[f28,f18]) ).
fof(f30,plain,
! [X0] : times(sK2,times(X0,sK2)) = times(sK0(sK2),X0),
inference(superposition,[],[f7,f15]) ).
fof(f32,plain,
! [X0] : times(sK1,times(X0,sK1)) = times(sK0(sK1),X0),
inference(superposition,[],[f7,f16]) ).
fof(f33,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(times(X0,times(X1,X2)),X3),
inference(superposition,[],[f7,f7]) ).
fof(f34,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(times(X1,X2),times(X3,X0)),
inference(forward_demodulation,[],[f33,f7]) ).
fof(f35,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(X2,times(times(X3,X0),X1)),
inference(forward_demodulation,[],[f34,f7]) ).
fof(f36,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(X2,times(X0,times(X1,X3))),
inference(forward_demodulation,[],[f35,f7]) ).
fof(f38,plain,
times(sK2,sK0(sK2)) = times(sK0(sK2),sK2),
inference(superposition,[],[f30,f15]) ).
fof(f40,plain,
! [X0,X1] : times(times(X0,sK2),times(X1,sK2)) = times(times(sK0(sK2),X0),X1),
inference(superposition,[],[f7,f30]) ).
fof(f41,plain,
! [X0,X1] : times(times(X0,sK2),times(X1,sK2)) = times(X0,times(X1,sK0(sK2))),
inference(forward_demodulation,[],[f40,f7]) ).
fof(f42,plain,
sK2 = times(sK0(sK2),sK2),
inference(forward_demodulation,[],[f38,f17]) ).
fof(f43,plain,
! [X0,X1] : times(X0,times(X1,sK0(sK2))) = times(sK2,times(times(X1,sK2),X0)),
inference(forward_demodulation,[],[f41,f7]) ).
fof(f44,plain,
! [X0,X1] : times(X0,times(X1,sK0(sK2))) = times(sK2,times(sK2,times(X0,X1))),
inference(forward_demodulation,[],[f43,f7]) ).
fof(f104,plain,
! [X0,X1] : times(sK1,times(sK1,times(X0,X1))) = times(X0,times(X1,sK0(sK1))),
inference(superposition,[],[f36,f16]) ).
fof(f105,plain,
! [X0,X1] : times(sK1,times(sK0(sK1),times(X0,X1))) = times(X0,times(X1,sK1)),
inference(superposition,[],[f36,f18]) ).
fof(f112,plain,
! [X0,X1] : times(X0,times(sK2,times(X1,sK2))) = times(X1,times(sK0(sK2),X0)),
inference(superposition,[],[f36,f30]) ).
fof(f143,plain,
! [X0,X1] : times(X1,times(sK0(sK2),X0)) = times(X0,times(sK0(sK2),X1)),
inference(forward_demodulation,[],[f112,f30]) ).
fof(f354,plain,
! [X0] : times(sK1,times(sK0(sK1),X0)) = times(X0,times(sK1,sK0(sK1))),
inference(superposition,[],[f104,f32]) ).
fof(f375,plain,
! [X0] : times(X0,sK1) = times(sK1,times(sK0(sK1),X0)),
inference(forward_demodulation,[],[f354,f18]) ).
fof(f471,plain,
times(sK1,times(sK0(sK1),sK2)) = times(sK2,times(sK0(sK2),sK1)),
inference(superposition,[],[f105,f17]) ).
fof(f497,plain,
times(sK1,times(sK0(sK2),sK2)) = times(sK1,times(sK0(sK1),sK2)),
inference(forward_demodulation,[],[f471,f143]) ).
fof(f519,plain,
times(sK2,sK1) = times(sK1,times(sK0(sK2),sK2)),
inference(forward_demodulation,[],[f497,f375]) ).
fof(f540,plain,
times(sK1,sK2) = times(sK2,sK1),
inference(forward_demodulation,[],[f519,f42]) ).
fof(f579,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK1,sK2))),
inference(superposition,[],[f29,f540]) ).
fof(f591,plain,
times(sK1,sK2) != times(sK1,times(sK2,sK0(sK2))),
inference(forward_demodulation,[],[f579,f44]) ).
fof(f596,plain,
times(sK1,sK2) != times(sK1,sK2),
inference(forward_demodulation,[],[f591,f17]) ).
fof(f597,plain,
$false,
inference(trivial_inequality_removal,[],[f596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n005.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 19:42:01 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.29 % (1082500)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1082517)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1024075:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (1082513)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1082517) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1082500-1082517"...
% 0.20/0.29 % (1082516)dis+10_1_sil=32000:sp=arity:random_seed=861392020:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1082515)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=271891385:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (1082512)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2888111846_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (1082513)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1880897793:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (1082519)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2299023453:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (1082518)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=643862221:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (1082517)...printing done.
% 0.20/0.29 % TRYING [1]
% 0.20/0.29 % TRYING [2]
% 0.20/0.29 % (1082517)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1082517)------------------------------
% 0.20/0.29 % (1082517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1082517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1082517)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1082517)Termination reason: Refutation
% 0.20/0.29 % (1082517)Time elapsed: 0.013 s
% 0.20/0.29 % (1082517)Peak memory usage: 12 MB
% 0.20/0.29 % (1082517)Instructions burned: 23 (million)
% 0.20/0.29 % (1082500)Success in time 0.056 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------