%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 10:16:02 AM UTC 2026
% Result : Theorem 5.11s 1.55s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 60 ( 54 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 45 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1,X2] : mult(mult(mult(X2,X1),X0),X1) = mult(X2,mult(mult(X1,X0),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X0,X1] : mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f9,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
fof(f10,axiom,
mult(op_a,op_b) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
fof(f11,axiom,
mult(op_b,op_a) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
fof(f12,conjecture,
! [X0] :
( mult(mult(X0,op_a),op_b) = X0
& mult(mult(X0,op_b),op_a) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f13,negated_conjecture,
~ ! [X0] :
( mult(mult(X0,op_a),op_b) = X0
& mult(mult(X0,op_b),op_a) = X0 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
? [X0] :
( mult(mult(X0,op_a),op_b) != X0
| mult(mult(X0,op_b),op_a) != X0 ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
( sK0 != mult(mult(sK0,op_a),op_b)
| sK0 != mult(mult(sK0,op_b),op_a) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f14]) ).
fof(f16,plain,
( sK0 != mult(mult(sK0,op_b),op_a)
| sK0 != mult(mult(sK0,op_a),op_b) ),
inference(cnf_transformation,[],[f15]) ).
fof(f17,plain,
! [X0,X1] : mult(X1,mult(X0,X0)) = mult(mult(X1,X0),X0),
inference(cnf_transformation,[],[f7]) ).
fof(f18,plain,
! [X2,X0,X1] : mult(mult(mult(X2,X1),X0),X1) = mult(X2,mult(mult(X1,X0),X1)),
inference(cnf_transformation,[],[f6]) ).
fof(f19,plain,
unit = mult(op_b,op_a),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
unit = mult(op_a,op_b),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[],[f8]) ).
fof(f26,plain,
mult(op_a,mult(op_b,op_b)) = mult(unit,op_b),
inference(superposition,[],[f17,f20]) ).
fof(f27,plain,
mult(op_b,mult(op_a,op_a)) = mult(unit,op_a),
inference(superposition,[],[f17,f19]) ).
fof(f30,plain,
op_a = mult(op_b,mult(op_a,op_a)),
inference(forward_demodulation,[],[f27,f21]) ).
fof(f31,plain,
op_b = mult(op_a,mult(op_b,op_b)),
inference(forward_demodulation,[],[f26,f21]) ).
fof(f36,plain,
! [X0] : mult(op_a,mult(mult(op_b,X0),op_b)) = mult(mult(unit,X0),op_b),
inference(superposition,[],[f18,f20]) ).
fof(f37,plain,
! [X0] : mult(op_b,mult(mult(op_a,X0),op_a)) = mult(mult(unit,X0),op_a),
inference(superposition,[],[f18,f19]) ).
fof(f39,plain,
! [X2,X0,X1] : mult(mult(X0,X1),mult(mult(X2,X1),X2)) = mult(mult(X0,mult(mult(X1,X2),X1)),X2),
inference(superposition,[],[f18,f18]) ).
fof(f52,plain,
! [X0] : mult(X0,op_a) = mult(op_b,mult(mult(op_a,X0),op_a)),
inference(forward_demodulation,[],[f37,f21]) ).
fof(f53,plain,
! [X0] : mult(X0,op_b) = mult(op_a,mult(mult(op_b,X0),op_b)),
inference(forward_demodulation,[],[f36,f21]) ).
fof(f63,plain,
mult(mult(op_b,op_b),op_a) = mult(op_b,mult(op_b,op_a)),
inference(superposition,[],[f52,f31]) ).
fof(f65,plain,
mult(op_a,op_a) = mult(op_b,mult(op_a,mult(op_a,op_a))),
inference(superposition,[],[f52,f17]) ).
fof(f69,plain,
mult(mult(op_b,op_b),op_a) = mult(op_b,unit),
inference(forward_demodulation,[],[f63,f19]) ).
fof(f70,plain,
op_b = mult(mult(op_b,op_b),op_a),
inference(forward_demodulation,[],[f69,f22]) ).
fof(f77,plain,
mult(mult(op_a,op_a),op_b) = mult(op_a,mult(op_a,op_b)),
inference(superposition,[],[f53,f30]) ).
fof(f80,plain,
mult(op_b,op_b) = mult(op_a,mult(op_b,mult(op_b,op_b))),
inference(superposition,[],[f53,f17]) ).
fof(f85,plain,
mult(op_a,unit) = mult(mult(op_a,op_a),op_b),
inference(forward_demodulation,[],[f77,f20]) ).
fof(f86,plain,
op_a = mult(mult(op_a,op_a),op_b),
inference(forward_demodulation,[],[f85,f22]) ).
fof(f371,plain,
! [X0] : mult(mult(X0,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))) = mult(mult(X0,mult(op_b,op_a)),mult(op_b,op_b)),
inference(superposition,[],[f39,f31]) ).
fof(f375,plain,
! [X0] : mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))) = mult(mult(X0,mult(op_a,op_b)),mult(op_a,op_a)),
inference(superposition,[],[f39,f30]) ).
fof(f428,plain,
! [X0] : mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))) = mult(mult(X0,unit),mult(op_a,op_a)),
inference(forward_demodulation,[],[f375,f20]) ).
fof(f431,plain,
! [X0] : mult(mult(X0,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))) = mult(mult(X0,unit),mult(op_b,op_b)),
inference(forward_demodulation,[],[f371,f19]) ).
fof(f447,plain,
! [X0] : mult(X0,mult(op_a,op_a)) = mult(mult(X0,op_b),mult(mult(mult(op_a,op_a),op_b),mult(op_a,op_a))),
inference(forward_demodulation,[],[f428,f22]) ).
fof(f449,plain,
! [X0] : mult(X0,mult(op_b,op_b)) = mult(mult(X0,op_a),mult(mult(mult(op_b,op_b),op_a),mult(op_b,op_b))),
inference(forward_demodulation,[],[f431,f22]) ).
fof(f462,plain,
! [X0] : mult(X0,mult(op_a,op_a)) = mult(mult(X0,op_b),mult(op_a,mult(op_a,op_a))),
inference(forward_demodulation,[],[f447,f86]) ).
fof(f463,plain,
! [X0] : mult(X0,mult(op_b,op_b)) = mult(mult(X0,op_a),mult(op_b,mult(op_b,op_b))),
inference(forward_demodulation,[],[f449,f70]) ).
fof(f1076,plain,
! [X0] : mult(X0,mult(mult(op_b,mult(op_a,mult(op_a,op_a))),op_b)) = mult(mult(X0,mult(op_a,op_a)),op_b),
inference(superposition,[],[f18,f462]) ).
fof(f1083,plain,
! [X0] : mult(X0,mult(mult(op_a,op_a),op_b)) = mult(mult(X0,mult(op_a,op_a)),op_b),
inference(forward_demodulation,[],[f1076,f65]) ).
fof(f1097,plain,
! [X0] : mult(X0,op_a) = mult(mult(X0,mult(op_a,op_a)),op_b),
inference(forward_demodulation,[],[f1083,f86]) ).
fof(f1137,plain,
! [X0] : mult(mult(X0,op_b),op_a) = mult(X0,mult(mult(op_b,mult(op_a,op_a)),op_b)),
inference(superposition,[],[f18,f1097]) ).
fof(f1154,plain,
! [X0] : mult(mult(X0,op_b),op_a) = mult(X0,mult(op_b,op_a)),
inference(forward_demodulation,[],[f1137,f1097]) ).
fof(f1176,plain,
! [X0] : mult(X0,unit) = mult(mult(X0,op_b),op_a),
inference(forward_demodulation,[],[f1154,f19]) ).
fof(f1189,plain,
! [X0] : mult(mult(X0,op_b),op_a) = X0,
inference(forward_demodulation,[],[f1176,f22]) ).
fof(f1220,plain,
! [X0] : mult(X0,mult(mult(op_a,mult(op_b,mult(op_b,op_b))),op_a)) = mult(mult(X0,mult(op_b,op_b)),op_a),
inference(superposition,[],[f18,f463]) ).
fof(f1227,plain,
! [X0] : mult(X0,mult(mult(op_b,op_b),op_a)) = mult(mult(X0,mult(op_b,op_b)),op_a),
inference(forward_demodulation,[],[f1220,f80]) ).
fof(f1241,plain,
! [X0] : mult(X0,op_b) = mult(mult(X0,mult(op_b,op_b)),op_a),
inference(forward_demodulation,[],[f1227,f70]) ).
fof(f1279,plain,
( sK0 != sK0
| sK0 != mult(mult(sK0,op_a),op_b) ),
inference(superposition,[],[f16,f1189]) ).
fof(f1294,plain,
sK0 != mult(mult(sK0,op_a),op_b),
inference(trivial_inequality_removal,[],[f1279]) ).
fof(f1385,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,mult(mult(op_a,mult(op_b,op_b)),op_a)),
inference(superposition,[],[f18,f1241]) ).
fof(f1403,plain,
! [X0] : mult(mult(X0,op_a),op_b) = mult(X0,mult(op_a,op_b)),
inference(forward_demodulation,[],[f1385,f1241]) ).
fof(f1425,plain,
! [X0] : mult(X0,unit) = mult(mult(X0,op_a),op_b),
inference(forward_demodulation,[],[f1403,f20]) ).
fof(f1438,plain,
! [X0] : mult(mult(X0,op_a),op_b) = X0,
inference(forward_demodulation,[],[f1425,f22]) ).
fof(f1524,plain,
sK0 != sK0,
inference(superposition,[],[f1294,f1438]) ).
fof(f1540,plain,
$false,
inference(trivial_inequality_removal,[],[f1524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP715+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 % Computer : n007.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sun Sep 27 10:35:09 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 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
% 5.11/1.55 % (1223577)Detected formulas, will run a generic FOF schedule.
% 5.11/1.55 % (1223587)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=986934574:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 5.11/1.55 % (1223587)Instruction limit reached!
% 5.11/1.55 % (1223587)------------------------------
% 5.11/1.55 % (1223587)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.55 % (1223587)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.55 % (1223587)CaDiCaL version: 2.1.3
% 5.11/1.55 % (1223587)Termination reason: Instruction limit
% 5.11/1.55 % (1223587)Termination phase: Saturation
% 5.11/1.55 % (1223587)Time elapsed: 0.052 s
% 5.11/1.55 % (1223587)Peak memory usage: 89 MB
% 5.11/1.55 % (1223587)Instructions burned: 139 (million)
% 5.11/1.55 % (1223583)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=1616432108:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 5.11/1.55 % (1223584)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=2359339948:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 5.11/1.55 % (1223582)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=3923490161:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 5.11/1.55 % (1223585)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3197143911:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 5.11/1.55 % (1223588)dis-21_1_sil=8000:lcm=predicate:random_seed=4101061999:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 5.11/1.55 % (1223586)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2656003637:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 5.11/1.55 % (1223585)Refutation not found, incomplete strategy
% 5.11/1.55 % (1223585)------------------------------
% 5.11/1.55 % (1223585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.55 % (1223585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.55 % (1223588)Refutation not found, incomplete strategy
% 5.11/1.55 % (1223588)------------------------------
% 5.11/1.55 % (1223588)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.55 % (1223585)CaDiCaL version: 2.1.3
% 5.11/1.55 % (1223585)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.55 % (1223585)Time elapsed: 0.002 s
% 5.11/1.55 % (1223588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.55 % (1223585)Peak memory usage: 88 MB
% 5.11/1.55 % (1223588)CaDiCaL version: 2.1.3
% 5.11/1.55 % (1223588)Termination reason: Refutation not found, incomplete strategy
% 5.11/1.55 % (1223588)Time elapsed: 0.002 s
% 5.11/1.55 % (1223588)Peak memory usage: 88 MB
% 5.11/1.55 % (1223586)First to succeed.
% 5.11/1.55 % (1223586)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1223577"
% 5.11/1.55 % (1223590)lrs+10_1_sil=8000:sp=occurrence:random_seed=3749467596:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 5.11/1.55 % (1223590)Instruction limit reached!
% 5.11/1.55 % (1223590)------------------------------
% 5.11/1.55 % (1223590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.11/1.55 % (1223590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.11/1.55 % (1223590)CaDiCaL version: 2.1.3
% 5.11/1.55 % (1223590)Termination reason: Instruction limit
% 5.11/1.55 % (1223590)Termination phase: Saturation
% 5.11/1.55 % (1223590)Time elapsed: 0.146 s
% 5.11/1.55 % (1223590)Peak memory usage: 91 MB
% 5.11/1.55 % (1223590)Instructions burned: 286 (million)
% 5.11/1.55 % (1223588)------------------------------
% 5.11/1.55 % (1223588)------------------------------
% 5.11/1.55 % (1223585)------------------------------
% 5.11/1.55 % (1223585)------------------------------
% 5.11/1.55 % (1223586)Refutation found. Thanks to Tanya!
% 5.11/1.55 % SZS status Theorem for theBenchmark
% 5.11/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 5.90/1.89 % (1223586)------------------------------
% 5.90/1.89 % (1223586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.90/1.89 % (1223586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.90/1.89 % (1223586)CaDiCaL version: 2.1.3
% 5.90/1.89 % (1223586)Termination reason: Refutation
% 5.90/1.89 % (1223586)Time elapsed: 0.063 s
% 5.90/1.89 % (1223586)Peak memory usage: 88 MB
% 5.90/1.89 % (1223586)Instructions burned: 65 (million)
% 5.90/1.89 % (1223586)------------------------------
% 5.90/1.89 % (1223586)------------------------------
% 5.90/1.89 % (1223577)Success in time 0.739 s
% 5.90/1.89 % Vampire exiting
%------------------------------------------------------------------------------