%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 09:19:19 AM UTC 2026
% Result : Theorem 3.62s 1.18s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 66 ( 43 unt; 0 def)
% Number of atoms : 109 ( 68 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 88 ( 45 ~; 25 |; 15 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 67 ( 60 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] : times(times(X0,X1),X2) = times(X1,times(X2,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] :
( element(X0)
<=> ? [X1] :
( times(X0,X1) = X0
& times(X0,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,conjecture,
! [X0,X1] :
( ( element(X0)
& element(X1) )
=> element(times(X0,X1)) ),
file('/export/starexec/sandbox2/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,
! [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(times(sK1,sK2))
& element(sK1)
& element(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[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] :
( times(X0,X0) = sK0(X0)
| ~ element(X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f13,plain,
! [X0] :
( times(X0,sK0(X0)) = X0
| ~ element(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,
element(sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
element(sK1),
inference(cnf_transformation,[],[f10]) ).
fof(f17,plain,
~ element(times(sK1,sK2)),
inference(cnf_transformation,[],[f10]) ).
fof(f18,plain,
! [X0] :
( element(X0)
| times(X0,times(X0,X0)) != X0 ),
inference(equality_resolution,[],[f14]) ).
fof(f19,plain,
times(sK1,sK2) != times(times(sK1,sK2),times(times(sK1,sK2),times(sK1,sK2))),
inference(resolution,[],[f18,f17]) ).
fof(f21,plain,
! [X0,X1] :
( ~ element(X0)
| times(X0,times(X1,X0)) = times(sK0(X0),X1) ),
inference(superposition,[],[f11,f12]) ).
fof(f22,plain,
! [X0,X1] :
( ~ element(X0)
| times(X0,X1) = times(sK0(X0),times(X1,X0)) ),
inference(superposition,[],[f11,f13]) ).
fof(f23,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(times(X0,times(X1,X2)),X3),
inference(superposition,[],[f11,f11]) ).
fof(f25,plain,
! [X0,X1] :
( ~ element(times(X0,X1))
| times(X0,X1) = times(X1,times(sK0(times(X0,X1)),X0)) ),
inference(superposition,[],[f11,f13]) ).
fof(f27,plain,
times(sK1,sK2) != times(sK2,times(times(times(sK1,sK2),times(sK1,sK2)),sK1)),
inference(superposition,[],[f19,f11]) ).
fof(f28,plain,
! [X0,X1] :
( times(X0,times(times(X1,X0),X1)) = sK0(times(X1,X0))
| ~ element(times(X1,X0)) ),
inference(superposition,[],[f12,f11]) ).
fof(f30,plain,
! [X0,X1] :
( ~ element(times(X1,X0))
| sK0(times(X1,X0)) = times(X0,times(X0,times(X1,X1))) ),
inference(forward_demodulation,[],[f28,f11]) ).
fof(f31,plain,
times(sK1,sK2) != times(sK2,times(times(sK1,sK2),times(sK1,times(sK1,sK2)))),
inference(forward_demodulation,[],[f27,f11]) ).
fof(f34,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(times(X1,X2),times(X3,X0)),
inference(forward_demodulation,[],[f23,f11]) ).
fof(f35,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(times(sK1,times(sK1,sK2)),sK1))),
inference(forward_demodulation,[],[f31,f11]) ).
fof(f37,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(X2,times(times(X3,X0),X1)),
inference(forward_demodulation,[],[f34,f11]) ).
fof(f38,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(times(sK1,sK2),times(sK1,sK1)))),
inference(forward_demodulation,[],[f35,f11]) ).
fof(f40,plain,
! [X2,X3,X0,X1] : times(X1,times(X3,times(X2,X0))) = times(X2,times(X0,times(X1,X3))),
inference(forward_demodulation,[],[f37,f11]) ).
fof(f41,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK2,times(times(sK1,sK1),sK1)))),
inference(forward_demodulation,[],[f38,f11]) ).
fof(f43,plain,
times(sK1,sK2) != times(sK2,times(sK2,times(sK2,times(sK1,times(sK1,sK1))))),
inference(forward_demodulation,[],[f41,f11]) ).
fof(f47,plain,
! [X0] : times(sK2,times(X0,sK2)) = times(sK0(sK2),X0),
inference(resolution,[],[f21,f15]) ).
fof(f48,plain,
! [X0] : times(sK1,times(X0,sK1)) = times(sK0(sK1),X0),
inference(resolution,[],[f21,f16]) ).
fof(f50,plain,
( times(sK0(sK2),sK2) = times(sK2,sK0(sK2))
| ~ element(sK2) ),
inference(superposition,[],[f47,f12]) ).
fof(f54,plain,
times(sK0(sK2),sK2) = times(sK2,sK0(sK2)),
inference(forward_subsumption_resolution,[],[f50,f15]) ).
fof(f57,plain,
! [X0] : times(sK2,X0) = times(sK0(sK2),times(X0,sK2)),
inference(resolution,[],[f22,f15]) ).
fof(f58,plain,
! [X0] : times(sK1,X0) = times(sK0(sK1),times(X0,sK1)),
inference(resolution,[],[f22,f16]) ).
fof(f235,plain,
! [X0] :
( ~ element(X0)
| times(sK0(X0),times(sK0(X0),X0)) = X0
| ~ element(X0) ),
inference(superposition,[],[f25,f13]) ).
fof(f242,plain,
! [X0] :
( ~ element(X0)
| times(sK0(X0),times(sK0(X0),X0)) = X0 ),
inference(duplicate_literal_removal,[],[f235]) ).
fof(f364,plain,
( sK0(sK2) = times(sK0(sK2),sK0(sK2))
| ~ element(sK2) ),
inference(superposition,[],[f57,f12]) ).
fof(f366,plain,
times(sK2,sK0(sK2)) = times(sK0(sK2),times(sK2,sK0(sK2))),
inference(superposition,[],[f57,f54]) ).
fof(f380,plain,
sK0(sK2) = times(sK0(sK2),sK0(sK2)),
inference(forward_subsumption_resolution,[],[f364,f15]) ).
fof(f503,plain,
sK2 = times(sK0(sK2),times(sK0(sK2),sK2)),
inference(resolution,[],[f242,f15]) ).
fof(f504,plain,
sK2 = times(sK2,sK0(sK2)),
inference(forward_demodulation,[],[f503,f57]) ).
fof(f552,plain,
( ~ element(sK2)
| sK0(sK2) = times(sK0(sK2),times(sK0(sK2),times(sK2,sK2))) ),
inference(superposition,[],[f30,f504]) ).
fof(f557,plain,
sK0(sK2) = times(sK0(sK2),times(sK0(sK2),times(sK2,sK2))),
inference(forward_subsumption_resolution,[],[f552,f15]) ).
fof(f558,plain,
sK0(sK2) = times(sK2,times(sK2,times(sK0(sK2),sK0(sK2)))),
inference(forward_demodulation,[],[f557,f40]) ).
fof(f559,plain,
sK0(sK2) = times(sK2,times(sK2,sK0(sK2))),
inference(forward_demodulation,[],[f558,f380]) ).
fof(f560,plain,
sK0(sK2) = times(sK2,sK2),
inference(forward_demodulation,[],[f559,f504]) ).
fof(f2691,plain,
sK2 = times(sK0(sK2),sK2),
inference(forward_demodulation,[],[f366,f504]) ).
fof(f2696,plain,
! [X0] : times(sK2,X0) = times(sK2,times(X0,sK0(sK2))),
inference(superposition,[],[f11,f2691]) ).
fof(f2715,plain,
! [X0,X1] : times(X1,times(sK2,X0)) = times(X0,times(sK0(sK2),times(X1,sK2))),
inference(superposition,[],[f40,f2696]) ).
fof(f2744,plain,
! [X0,X1] : times(X0,times(sK2,X1)) = times(X1,times(sK2,X0)),
inference(forward_demodulation,[],[f2715,f57]) ).
fof(f2779,plain,
! [X0] : times(X0,sK0(sK2)) = times(sK2,times(sK2,X0)),
inference(superposition,[],[f2744,f560]) ).
fof(f3459,plain,
times(sK1,sK2) != times(times(sK2,times(sK1,times(sK1,sK1))),sK0(sK2)),
inference(superposition,[],[f43,f2779]) ).
fof(f3530,plain,
times(sK1,sK2) != times(times(sK1,times(sK1,sK1)),times(sK0(sK2),sK2)),
inference(forward_demodulation,[],[f3459,f11]) ).
fof(f3578,plain,
times(sK1,sK2) != times(times(sK1,sK1),times(times(sK0(sK2),sK2),sK1)),
inference(forward_demodulation,[],[f3530,f11]) ).
fof(f3617,plain,
times(sK1,sK2) != times(sK1,times(times(times(sK0(sK2),sK2),sK1),sK1)),
inference(forward_demodulation,[],[f3578,f11]) ).
fof(f3647,plain,
times(sK1,sK2) != times(sK0(sK1),times(times(sK0(sK2),sK2),sK1)),
inference(forward_demodulation,[],[f3617,f48]) ).
fof(f3667,plain,
times(sK1,sK2) != times(sK1,times(sK0(sK2),sK2)),
inference(forward_demodulation,[],[f3647,f58]) ).
fof(f3672,plain,
times(sK1,sK2) != times(sK1,times(sK2,sK0(sK2))),
inference(forward_demodulation,[],[f3667,f54]) ).
fof(f3674,plain,
times(sK1,sK2) != times(sK1,sK2),
inference(forward_demodulation,[],[f3672,f504]) ).
fof(f3675,plain,
$false,
inference(trivial_inequality_removal,[],[f3674]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG210+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n006.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 19:41:55 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 3.62/1.18 % (99334)Detected formulas, will run a generic FOF schedule.
% 3.62/1.18 % (99343)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1246354621:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.62/1.18 % (99343)Instruction limit reached!
% 3.62/1.18 % (99343)------------------------------
% 3.62/1.18 % (99343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.18 % (99343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.18 % (99343)CaDiCaL version: 2.1.3
% 3.62/1.18 % (99343)Termination reason: Instruction limit
% 3.62/1.18 % (99343)Termination phase: Saturation
% 3.62/1.18 % (99343)Time elapsed: 0.035 s
% 3.62/1.18 % (99343)Peak memory usage: 89 MB
% 3.62/1.18 % (99343)Instructions burned: 119 (million)
% 3.62/1.18 % (99341)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=845224350:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.62/1.18 % (99342)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4261056964:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.62/1.18 % (99339)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=3298216439:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.62/1.18 % (99340)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=819046506:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.62/1.18 % (99342)Refutation not found, incomplete strategy
% 3.62/1.18 % (99342)------------------------------
% 3.62/1.18 % (99342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.18 % (99342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.18 % (99342)CaDiCaL version: 2.1.3
% 3.62/1.18 % (99342)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.18 % (99342)Time elapsed: 0.001 s
% 3.62/1.18 % (99342)Peak memory usage: 88 MB
% 3.62/1.18 % (99345)dis-21_1_sil=8000:lcm=predicate:random_seed=3635088390:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.62/1.18 % (99344)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3233407669:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.62/1.18 % (99345)Refutation not found, incomplete strategy
% 3.62/1.18 % (99345)------------------------------
% 3.62/1.18 % (99345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.62/1.18 % (99345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.62/1.18 % (99345)CaDiCaL version: 2.1.3
% 3.62/1.18 % (99345)Termination reason: Refutation not found, incomplete strategy
% 3.62/1.18 % (99345)Time elapsed: 0.001 s
% 3.62/1.18 % (99345)Peak memory usage: 88 MB
% 3.62/1.18 % (99344)First to succeed.
% 3.62/1.18 % (99344)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-99334"
% 3.62/1.18 % (99347)lrs+10_1_sil=8000:sp=occurrence:random_seed=399893431:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.62/1.18 % (99347)Also succeeded, but the first one will report.
% 3.62/1.18 % (99342)------------------------------
% 3.62/1.18 % (99342)------------------------------
% 3.62/1.18 % (99345)------------------------------
% 3.62/1.18 % (99345)------------------------------
% 3.62/1.18 % (99344)Refutation found. Thanks to Tanya!
% 3.62/1.18 % SZS status Theorem for theBenchmark
% 3.62/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 4.16/1.37 % (99344)------------------------------
% 4.16/1.37 % (99344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.16/1.37 % (99344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.16/1.37 % (99344)CaDiCaL version: 2.1.3
% 4.16/1.37 % (99344)Termination reason: Refutation
% 4.16/1.37 % (99344)Time elapsed: 0.072 s
% 4.16/1.37 % (99344)Peak memory usage: 90 MB
% 4.16/1.37 % (99344)Instructions burned: 136 (million)
% 4.16/1.37 % (99344)------------------------------
% 4.16/1.37 % (99344)------------------------------
% 4.16/1.37 % (99334)Success in time 0.499 s
% 4.16/1.37 % Vampire exiting
%------------------------------------------------------------------------------