%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 10:15:27 AM UTC 2026
% Result : Theorem 6.04s 2.00s
% Output : Refutation 6.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 18 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 0 con; 1-2 aty)
% Number of variables : 48 ( 45 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f5,axiom,
! [X0,X1,X2] : mult(mult(X2,X1),mult(X0,X2)) = mult(mult(X2,mult(X1,X0)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,conjecture,
? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f7,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X1,X0) = X1
& mult(X0,X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0] :
? [X1] :
( mult(X1,X0) != X1
| mult(X0,X1) != X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f9,plain,
! [X0] :
( sK0(X0) != mult(sK0(X0),X0)
| sK0(X0) != mult(X0,sK0(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f8]) ).
fof(f10,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1] : ld(X1,mult(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f14,plain,
! [X2,X0,X1] : mult(mult(X2,X1),mult(X0,X2)) = mult(mult(X2,mult(X1,X0)),X2),
inference(cnf_transformation,[],[f5]) ).
fof(f15,plain,
! [X0] :
( sK0(X0) != mult(sK0(X0),X0)
| sK0(X0) != mult(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f9]) ).
fof(f18,plain,
! [X2,X0,X1] : mult(mult(X1,X2),mult(ld(X2,X0),X1)) = mult(mult(X1,X0),X1),
inference(superposition,[],[f14,f10]) ).
fof(f19,plain,
! [X2,X0,X1] : mult(mult(X1,X0),X1) = mult(mult(X1,rd(X0,X2)),mult(X2,X1)),
inference(superposition,[],[f14,f12]) ).
fof(f40,plain,
! [X2,X0,X1] : mult(ld(X2,X1),X0) = ld(mult(X0,X2),mult(mult(X0,X1),X0)),
inference(superposition,[],[f11,f18]) ).
fof(f46,plain,
! [X2,X0,X1] : mult(mult(ld(X1,X0),X2),ld(X1,X0)) = mult(mult(ld(X1,X0),rd(X2,X1)),X0),
inference(superposition,[],[f19,f10]) ).
fof(f354,plain,
! [X0,X1] : mult(ld(X1,X1),X0) = X0,
inference(superposition,[],[f40,f11]) ).
fof(f865,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(mult(ld(X1,X1),X0),ld(X1,X1)),
inference(superposition,[],[f46,f354]) ).
fof(f911,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[],[f865,f354]) ).
fof(f923,plain,
! [X0,X1] : mult(X0,ld(X1,X1)) = X0,
inference(forward_demodulation,[],[f911,f12]) ).
fof(f974,plain,
! [X0] :
( sK0(ld(X0,X0)) != sK0(ld(X0,X0))
| sK0(ld(X0,X0)) != mult(ld(X0,X0),sK0(ld(X0,X0))) ),
inference(superposition,[],[f15,f923]) ).
fof(f975,plain,
! [X0] : sK0(ld(X0,X0)) != mult(ld(X0,X0),sK0(ld(X0,X0))),
inference(trivial_inequality_removal,[],[f974]) ).
fof(f976,plain,
$false,
inference(forward_subsumption_resolution,[],[f975,f354]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP656+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 10:32:21 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.04/2.00 % (3314040)Detected formulas, will run a generic FOF schedule.
% 6.04/2.00 % (3314051)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2457462862:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.04/2.00 % (3314051)Instruction limit reached!
% 6.04/2.00 % (3314051)------------------------------
% 6.04/2.00 % (3314051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/2.00 % (3314051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/2.00 % (3314051)CaDiCaL version: 2.1.3
% 6.04/2.00 % (3314051)Termination reason: Instruction limit
% 6.04/2.00 % (3314051)Termination phase: Saturation
% 6.04/2.00 % (3314051)Time elapsed: 0.057 s
% 6.04/2.00 % (3314051)Peak memory usage: 89 MB
% 6.04/2.00 % (3314051)Instructions burned: 120 (million)
% 6.04/2.00 % (3314047)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=1786709571:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.04/2.00 % (3314049)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=868278625:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.04/2.00 % (3314052)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=592767706:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.04/2.00 % (3314050)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1550681616:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.04/2.00 % (3314048)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=243736703:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.04/2.00 % (3314053)dis-21_1_sil=8000:lcm=predicate:random_seed=3369636770: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)
% 6.04/2.00 % (3314050)Refutation not found, incomplete strategy
% 6.04/2.00 % (3314050)------------------------------
% 6.04/2.00 % (3314050)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/2.00 % (3314050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/2.00 % (3314050)CaDiCaL version: 2.1.3
% 6.04/2.00 % (3314050)Termination reason: Refutation not found, incomplete strategy
% 6.04/2.00 % (3314050)Time elapsed: 0.001 s
% 6.04/2.00 % (3314050)Peak memory usage: 88 MB
% 6.04/2.00 % (3314053)Refutation not found, incomplete strategy
% 6.04/2.00 % (3314053)------------------------------
% 6.04/2.00 % (3314053)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/2.00 % (3314053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/2.00 % (3314053)CaDiCaL version: 2.1.3
% 6.04/2.00 % (3314053)Termination reason: Refutation not found, incomplete strategy
% 6.04/2.00 % (3314053)Time elapsed: 0.002 s
% 6.04/2.00 % (3314053)Peak memory usage: 88 MB
% 6.04/2.00 % (3314052)First to succeed.
% 6.04/2.00 % (3314052)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3314040"
% 6.04/2.00 % (3314061)lrs+10_1_sil=8000:sp=occurrence:random_seed=155263346:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.04/2.00 % (3314061)Also succeeded, but the first one will report.
% 6.04/2.00 % (3314053)------------------------------
% 6.04/2.00 % (3314053)------------------------------
% 6.04/2.00 % (3314050)------------------------------
% 6.04/2.00 % (3314050)------------------------------
% 6.04/2.00 % (3314052)Refutation found. Thanks to Tanya!
% 6.04/2.00 % SZS status Theorem for theBenchmark
% 6.04/2.00 % SZS output start Proof for theBenchmark
% See solution above
% 6.04/2.00 % (3314052)------------------------------
% 6.04/2.00 % (3314052)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.04/2.00 % (3314052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.04/2.00 % (3314052)CaDiCaL version: 2.1.3
% 6.04/2.00 % (3314052)Termination reason: Refutation
% 6.04/2.00 % (3314052)Time elapsed: 0.053 s
% 6.04/2.00 % (3314052)Peak memory usage: 89 MB
% 6.04/2.00 % (3314052)Instructions burned: 53 (million)
% 6.04/2.00 % (3314052)------------------------------
% 6.04/2.00 % (3314052)------------------------------
% 6.04/2.00 % (3314040)Success in time 0.741 s
% 6.04/2.00 % Vampire exiting
%------------------------------------------------------------------------------