%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP747+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 : n014.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 10:16:05 AM UTC 2026
% Result : Theorem 3.98s 1.49s
% Output : Refutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 18 unt; 2 def)
% Number of atoms : 86 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 26 ~; 34 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f6,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( mult(mult(X0,X1),X2) = mult(X0,mult(X2,X1))
& mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2)) )
| ( mult(mult(X0,X1),X2) = mult(mult(X0,X2),X1)
& mult(X0,mult(X1,X2)) = mult(X0,mult(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f9,conjecture,
mult(mult(a,b),c) = mult(a,mult(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f10,negated_conjecture,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(flattening,[],[f10]) ).
fof(f14,plain,
! [X0,X1] : mult(rd(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X0,X1] : rd(mult(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f17,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f19,plain,
! [X2,X0,X1] :
( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
| mult(X0,mult(X2,X1)) = mult(X0,mult(X1,X2)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f20,plain,
! [X2,X0,X1] :
( mult(mult(X0,X2),X1) = mult(X0,mult(X1,X2))
| mult(mult(X0,X1),X2) = mult(mult(X0,X2),X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
mult(mult(a,b),c) != mult(a,mult(b,c)),
inference(cnf_transformation,[],[f11]) ).
fof(f65,plain,
! [X0,X1] :
( mult(X0,X1) = mult(unit,mult(X1,X0))
| mult(unit,mult(X1,X0)) = mult(unit,mult(X0,X1)) ),
inference(superposition,[],[f19,f17]) ).
fof(f77,plain,
! [X0,X1] :
( mult(X1,X0) = mult(X0,X1)
| mult(unit,mult(X1,X0)) = mult(unit,mult(X0,X1)) ),
inference(forward_demodulation,[],[f65,f17]) ).
fof(f78,plain,
! [X0,X1] :
( mult(X0,X1) = mult(unit,mult(X1,X0))
| mult(X1,X0) = mult(X0,X1) ),
inference(forward_demodulation,[],[f77,f17]) ).
fof(f79,plain,
! [X0,X1] :
( mult(X1,X0) = mult(X0,X1)
| mult(X1,X0) = mult(X0,X1) ),
inference(forward_demodulation,[],[f78,f17]) ).
fof(f80,plain,
! [X0,X1] : mult(X1,X0) = mult(X0,X1),
inference(duplicate_literal_removal,[],[f79]) ).
fof(f91,plain,
( mult(a,mult(b,c)) != mult(a,mult(c,b))
| mult(mult(a,b),c) = mult(mult(a,c),b) ),
inference(superposition,[],[f23,f20]) ).
fof(f98,plain,
! [X2,X0,X1] :
( mult(X0,X2) = rd(mult(X0,mult(X1,X2)),X1)
| mult(mult(X0,X1),X2) = mult(mult(X0,X2),X1) ),
inference(superposition,[],[f15,f20]) ).
fof(f104,definition,
( spl0_1
<=> mult(mult(a,b),c) = mult(mult(a,c),b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f106,plain,
( mult(mult(a,b),c) = mult(mult(a,c),b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f108,definition,
( spl0_2
<=> mult(a,mult(b,c)) = mult(a,mult(c,b)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f110,plain,
( mult(a,mult(b,c)) != mult(a,mult(c,b))
| spl0_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f111,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f91,f108,f104]) ).
fof(f142,plain,
mult(a,mult(b,c)) != mult(c,mult(a,b)),
inference(superposition,[],[f23,f80]) ).
fof(f149,plain,
( mult(a,mult(b,c)) != mult(a,mult(b,c))
| spl0_2 ),
inference(superposition,[],[f110,f80]) ).
fof(f166,plain,
( $false
| spl0_2 ),
inference(trivial_inequality_removal,[],[f149]) ).
fof(f167,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f166]) ).
fof(f180,plain,
( mult(mult(a,b),c) = mult(b,mult(a,c))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f106,f80]) ).
fof(f181,plain,
( mult(c,mult(a,b)) = mult(b,mult(a,c))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f180,f80]) ).
fof(f190,plain,
( mult(a,mult(b,c)) != mult(b,mult(a,c))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f142,f181]) ).
fof(f1460,plain,
( mult(c,b) = rd(mult(b,mult(a,c)),a)
| mult(mult(c,b),a) = mult(mult(c,a),b)
| ~ spl0_1 ),
inference(superposition,[],[f98,f181]) ).
fof(f1481,plain,
( mult(b,c) = rd(mult(b,mult(a,c)),a)
| mult(mult(c,b),a) = mult(mult(c,a),b)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1460,f80]) ).
fof(f1504,plain,
( mult(mult(c,b),a) = mult(b,mult(c,a))
| mult(b,c) = rd(mult(b,mult(a,c)),a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1481,f80]) ).
fof(f1517,plain,
( mult(mult(c,b),a) = mult(b,mult(a,c))
| mult(b,c) = rd(mult(b,mult(a,c)),a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1504,f80]) ).
fof(f1525,plain,
( mult(a,mult(c,b)) = mult(b,mult(a,c))
| mult(b,c) = rd(mult(b,mult(a,c)),a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1517,f80]) ).
fof(f1530,plain,
( mult(a,mult(b,c)) = mult(b,mult(a,c))
| mult(b,c) = rd(mult(b,mult(a,c)),a)
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1525,f80]) ).
fof(f1543,plain,
( mult(b,c) = rd(mult(b,mult(a,c)),a)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1530,f190]) ).
fof(f1759,plain,
( mult(b,mult(a,c)) = mult(mult(b,c),a)
| ~ spl0_1 ),
inference(superposition,[],[f14,f1543]) ).
fof(f1760,plain,
( mult(a,mult(b,c)) = mult(b,mult(a,c))
| ~ spl0_1 ),
inference(forward_demodulation,[],[f1759,f80]) ).
fof(f1762,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1760,f190]) ).
fof(f1763,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1762]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f111]) ).
cnf(s3,plain,
spl0_2,
inference(sat_conversion,[],[f167]) ).
cnf(s10,plain,
~ spl0_1,
inference(sat_conversion,[],[f1763]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s3,s10]) ).
fof(f1764,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP747+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:41:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.98/1.49 % (608270)Detected formulas, will run a generic FOF schedule.
% 3.98/1.49 % (608279)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2524873747:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.98/1.49 % (608279)Instruction limit reached!
% 3.98/1.49 % (608279)------------------------------
% 3.98/1.49 % (608279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.49 % (608279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.49 % (608279)CaDiCaL version: 2.1.3
% 3.98/1.49 % (608279)Termination reason: Instruction limit
% 3.98/1.49 % (608279)Termination phase: Saturation
% 3.98/1.49 % (608279)Time elapsed: 0.034 s
% 3.98/1.49 % (608279)Peak memory usage: 88 MB
% 3.98/1.49 % (608279)Instructions burned: 122 (million)
% 3.98/1.49 % (608277)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=1331854650:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.98/1.49 % (608281)dis-21_1_sil=8000:lcm=predicate:random_seed=612910116: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)
% 3.98/1.49 % (608278)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3010313213:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.98/1.49 % (608275)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=3680100744:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.98/1.49 % (608276)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=2025925830:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.98/1.49 % (608278)Refutation not found, incomplete strategy
% 3.98/1.49 % (608278)------------------------------
% 3.98/1.49 % (608278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.49 % (608281)Refutation not found, incomplete strategy
% 3.98/1.49 % (608281)------------------------------
% 3.98/1.49 % (608281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.49 % (608278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.49 % (608278)CaDiCaL version: 2.1.3
% 3.98/1.49 % (608278)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.49 % (608278)Time elapsed: 0.001 s
% 3.98/1.49 % (608281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.49 % (608281)CaDiCaL version: 2.1.3
% 3.98/1.49 % (608278)Peak memory usage: 88 MB
% 3.98/1.49 % (608281)Termination reason: Refutation not found, incomplete strategy
% 3.98/1.49 % (608281)Time elapsed: 0.001 s
% 3.98/1.49 % (608281)Peak memory usage: 88 MB
% 3.98/1.49 % (608281)Instructions burned: 1 (million)
% 3.98/1.49 % (608280)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3527266136:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.98/1.49 % (608280)First to succeed.
% 3.98/1.49 % (608280)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-608270"
% 3.98/1.49 % (608283)lrs+10_1_sil=8000:sp=occurrence:random_seed=282925601:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.98/1.49 % (608283)Instruction limit reached!
% 3.98/1.49 % (608283)------------------------------
% 3.98/1.49 % (608283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.49 % (608283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.49 % (608283)CaDiCaL version: 2.1.3
% 3.98/1.49 % (608283)Termination reason: Instruction limit
% 3.98/1.49 % (608283)Termination phase: Saturation
% 3.98/1.49 % (608283)Time elapsed: 0.087 s
% 3.98/1.49 % (608283)Peak memory usage: 90 MB
% 3.98/1.49 % (608283)Instructions burned: 286 (million)
% 3.98/1.49 % (608278)------------------------------
% 3.98/1.49 % (608278)------------------------------
% 3.98/1.49 % (608281)------------------------------
% 3.98/1.49 % (608281)------------------------------
% 3.98/1.49 % (608280)Refutation found. Thanks to Tanya!
% 3.98/1.49 % SZS status Theorem for theBenchmark
% 3.98/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.98/1.49 % (608280)------------------------------
% 3.98/1.49 % (608280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.98/1.49 % (608280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.98/1.49 % (608280)CaDiCaL version: 2.1.3
% 3.98/1.49 % (608280)Termination reason: Refutation
% 3.98/1.49 % (608280)Time elapsed: 0.058 s
% 3.98/1.49 % (608280)Peak memory usage: 90 MB
% 3.98/1.49 % (608280)Instructions burned: 98 (million)
% 3.98/1.49 % (608280)------------------------------
% 3.98/1.49 % (608280)------------------------------
% 3.98/1.49 % (608270)Success in time 0.487 s
% 3.98/1.49 % Vampire exiting
%------------------------------------------------------------------------------