%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP704+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 : n008.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 10:16:00 AM UTC 2026
% Result : Theorem 4.50s 1.69s
% Output : Refutation 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 34 ( 33 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 9 |; 4 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f8,axiom,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f10,axiom,
! [X0,X1] : mult(X1,mult(op_c,X0)) = mult(mult(X1,op_c),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f13,axiom,
! [X0,X1] : op_f = mult(X1,mult(X0,ld(mult(X1,X0),op_c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f13) ).
fof(f14,conjecture,
! [X0,X1] :
( mult(op_f,mult(X0,X1)) = mult(mult(op_f,X0),X1)
& mult(X0,mult(X1,op_f)) = mult(mult(X0,X1),op_f)
& mult(X0,mult(op_f,X1)) = mult(mult(X0,op_f),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f15,negated_conjecture,
~ ! [X0,X1] :
( mult(op_f,mult(X0,X1)) = mult(mult(op_f,X0),X1)
& mult(X0,mult(X1,op_f)) = mult(mult(X0,X1),op_f)
& mult(X0,mult(op_f,X1)) = mult(mult(X0,op_f),X1) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
fof(f16,plain,
? [X0,X1] :
( mult(op_f,mult(X0,X1)) != mult(mult(op_f,X0),X1)
| mult(X0,mult(X1,op_f)) != mult(mult(X0,X1),op_f)
| mult(X0,mult(op_f,X1)) != mult(mult(X0,op_f),X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
( mult(op_f,mult(sK0,sK1)) != mult(mult(op_f,sK0),sK1)
| mult(sK0,mult(sK1,op_f)) != mult(mult(sK0,sK1),op_f)
| mult(sK0,mult(op_f,sK1)) != mult(mult(sK0,op_f),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
fof(f18,plain,
( mult(sK0,mult(sK1,op_f)) != mult(mult(sK0,sK1),op_f)
| mult(op_f,mult(sK0,sK1)) != mult(mult(op_f,sK0),sK1)
| mult(sK0,mult(op_f,sK1)) != mult(mult(sK0,op_f),sK1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f20,plain,
! [X0,X1] : op_f = mult(X1,mult(X0,ld(mult(X1,X0),op_c))),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] : mult(X1,ld(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0,X1] : mult(X1,mult(op_c,X0)) = mult(mult(X1,op_c),X0),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
! [X0,X1] : mult(X1,mult(X0,op_c)) = mult(mult(X1,X0),op_c),
inference(cnf_transformation,[],[f9]) ).
fof(f25,plain,
! [X0,X1] : mult(op_c,mult(X1,X0)) = mult(mult(op_c,X1),X0),
inference(cnf_transformation,[],[f8]) ).
fof(f30,plain,
! [X0,X1] : mult(X1,mult(op_c,ld(mult(X1,op_c),X0))) = X0,
inference(superposition,[],[f23,f22]) ).
fof(f148,plain,
op_c = op_f,
inference(superposition,[],[f30,f20]) ).
fof(f201,plain,
( mult(sK0,mult(sK1,op_c)) != mult(mult(sK0,sK1),op_c)
| mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| mult(sK0,mult(op_c,sK1)) != mult(mult(sK0,op_c),sK1) ),
inference(superposition,[],[f18,f148]) ).
fof(f202,plain,
( mult(op_c,mult(sK0,sK1)) != mult(mult(op_c,sK0),sK1)
| mult(sK0,mult(op_c,sK1)) != mult(mult(sK0,op_c),sK1) ),
inference(forward_subsumption_resolution,[],[f201,f24]) ).
fof(f203,plain,
mult(sK0,mult(op_c,sK1)) != mult(mult(sK0,op_c),sK1),
inference(forward_subsumption_resolution,[],[f202,f25]) ).
fof(f204,plain,
$false,
inference(forward_subsumption_resolution,[],[f203,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP704+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 10:37:39 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 4.50/1.69 % (1032555)Detected formulas, will run a generic FOF schedule.
% 4.50/1.69 % (1032667)dis-21_1_sil=8000:lcm=predicate:random_seed=1081420279: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)
% 4.50/1.69 % (1032667)Refutation not found, incomplete strategy
% 4.50/1.69 % (1032667)------------------------------
% 4.50/1.69 % (1032667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.69 % (1032667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.69 % (1032667)CaDiCaL version: 2.1.3
% 4.50/1.69 % (1032667)Termination reason: Refutation not found, incomplete strategy
% 4.50/1.69 % (1032667)Time elapsed: 0.001 s
% 4.50/1.69 % (1032667)Peak memory usage: 88 MB
% 4.50/1.69 % (1032667)Instructions burned: 1 (million)
% 4.50/1.69 % (1032661)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=1681454591:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.50/1.69 % (1032664)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3022986187:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.50/1.69 % (1032665)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2214779518:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.50/1.69 % (1032663)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=2212681801:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.50/1.69 % (1032666)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1385950274:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.50/1.69 % (1032662)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=4094024235:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.50/1.69 % (1032665)First to succeed.
% 4.50/1.69 % (1032666)Also succeeded, but the first one will report.
% 4.50/1.69 % (1032665)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1032555"
% 4.50/1.69 % (1032664)Instruction limit reached!
% 4.50/1.69 % (1032664)------------------------------
% 4.50/1.69 % (1032664)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.69 % (1032664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.69 % (1032664)CaDiCaL version: 2.1.3
% 4.50/1.69 % (1032664)Termination reason: Instruction limit
% 4.50/1.69 % (1032664)Termination phase: Saturation
% 4.50/1.69 % (1032664)Time elapsed: 0.062 s
% 4.50/1.69 % (1032664)Peak memory usage: 89 MB
% 4.50/1.69 % (1032664)Instructions burned: 110 (million)
% 4.50/1.69 % (1032667)------------------------------
% 4.50/1.69 % (1032667)------------------------------
% 4.50/1.69 % (1032681)lrs+10_1_sil=8000:sp=occurrence:random_seed=1672015988:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.50/1.69 % (1032681)Also succeeded, but the first one will report.
% 4.50/1.69 % (1032665)Refutation found. Thanks to Tanya!
% 4.50/1.69 % SZS status Theorem for theBenchmark
% 4.50/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 4.50/1.69 % (1032665)------------------------------
% 4.50/1.69 % (1032665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.50/1.69 % (1032665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.50/1.69 % (1032665)CaDiCaL version: 2.1.3
% 4.50/1.69 % (1032665)Termination reason: Refutation
% 4.50/1.69 % (1032665)Time elapsed: 0.007 s
% 4.50/1.69 % (1032665)Peak memory usage: 88 MB
% 4.50/1.69 % (1032665)Instructions burned: 9 (million)
% 4.50/1.69 % (1032665)------------------------------
% 4.50/1.69 % (1032665)------------------------------
% 4.50/1.69 % (1032555)Success in time 0.542 s
% 4.50/1.69 % Vampire exiting
%------------------------------------------------------------------------------