%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP715-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 : Unsatisfiable 6.56s 1.91s
% Output : Refutation 6.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 29 unt; 9 def)
% Number of atoms : 150 ( 47 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 162 ( 80 ~; 75 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f8,axiom,
! [X0,X1] : mult(X0,mult(X1,X1)) = mult(mult(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f9,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f10,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f11,axiom,
mult(op_a,op_b) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f12,plain,
unit = mult(op_a,op_b),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
mult(op_b,op_a) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f14,plain,
unit = mult(op_b,op_a),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
mult(mult(x0,op_a),op_b) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f16,plain,
x0 != mult(mult(x0,op_a),op_b),
inference(reorient_equations,[],[f15]) ).
fof(f17,definition,
sF0 = mult(x0,op_a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f18,plain,
mult(x0,op_a) = sF0,
inference(reorient_equations,[],[f17]) ).
fof(f19,definition,
sF1 = mult(sF0,op_b),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f20,plain,
mult(sF0,op_b) = sF1,
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
x0 != sF1,
inference(definition_folding,[],[f16,f20,f18]) ).
fof(f23,definition,
( spl2_1
<=> mult(x0,op_a) = sF0 ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f25,plain,
( mult(x0,op_a) = sF0
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f26,plain,
spl2_1,
inference(avatar_split_clause,[],[f18,f23]) ).
fof(f28,definition,
( spl2_2
<=> unit = mult(op_b,op_a) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f30,plain,
( unit = mult(op_b,op_a)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
spl2_2,
inference(avatar_split_clause,[],[f14,f28]) ).
fof(f33,definition,
( spl2_3
<=> unit = mult(op_a,op_b) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f35,plain,
( unit = mult(op_a,op_b)
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
spl2_3,
inference(avatar_split_clause,[],[f12,f33]) ).
fof(f38,definition,
( spl2_4
<=> x0 = sF1 ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f40,plain,
( x0 != sF1
| spl2_4 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,plain,
~ spl2_4,
inference(avatar_split_clause,[],[f21,f38]) ).
fof(f42,plain,
( ! [X0] : mult(x0,mult(mult(op_a,X0),op_a)) = mult(mult(sF0,X0),op_a)
| ~ spl2_1 ),
inference(superposition,[],[f7,f25]) ).
fof(f48,definition,
( spl2_5
<=> mult(sF0,op_b) = sF1 ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f50,plain,
( mult(sF0,op_b) = sF1
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f51,plain,
spl2_5,
inference(avatar_split_clause,[],[f20,f48]) ).
fof(f72,plain,
( mult(sF0,mult(op_b,op_b)) = mult(sF1,op_b)
| ~ spl2_5 ),
inference(superposition,[],[f8,f50]) ).
fof(f89,plain,
( mult(mult(sF0,op_b),op_a) = mult(x0,mult(unit,op_a))
| ~ spl2_1
| ~ spl2_3 ),
inference(superposition,[],[f42,f35]) ).
fof(f90,plain,
( mult(op_a,mult(op_b,op_b)) = mult(unit,op_b)
| ~ spl2_3 ),
inference(superposition,[],[f8,f35]) ).
fof(f93,plain,
( op_b = mult(op_a,mult(op_b,op_b))
| ~ spl2_3 ),
inference(forward_demodulation,[],[f90,f10]) ).
fof(f94,plain,
( mult(x0,op_a) = mult(mult(sF0,op_b),op_a)
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[],[f89,f10]) ).
fof(f95,plain,
( mult(x0,op_a) = mult(sF1,op_a)
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(forward_demodulation,[],[f94,f50]) ).
fof(f96,plain,
( sF0 = mult(sF1,op_a)
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(forward_demodulation,[],[f95,f25]) ).
fof(f98,definition,
( spl2_6
<=> sF0 = mult(sF1,op_a) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f100,plain,
( sF0 = mult(sF1,op_a)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f98]) ).
fof(f101,plain,
( spl2_6
| ~ spl2_1
| ~ spl2_3
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f96,f48,f33,f23,f98]) ).
fof(f103,plain,
( ! [X0] : mult(mult(sF0,X0),op_a) = mult(sF1,mult(mult(op_a,X0),op_a))
| ~ spl2_6 ),
inference(superposition,[],[f7,f100]) ).
fof(f190,definition,
( spl2_8
<=> op_b = mult(op_a,mult(op_b,op_b)) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f192,plain,
( op_b = mult(op_a,mult(op_b,op_b))
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f193,plain,
( spl2_8
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f93,f33,f190]) ).
fof(f194,plain,
( mult(mult(sF0,mult(op_b,op_b)),op_a) = mult(x0,mult(op_b,op_a))
| ~ spl2_1
| ~ spl2_8 ),
inference(superposition,[],[f42,f192]) ).
fof(f201,plain,
( mult(mult(sF0,mult(op_b,op_b)),op_a) = mult(x0,unit)
| ~ spl2_1
| ~ spl2_2
| ~ spl2_8 ),
inference(forward_demodulation,[],[f194,f30]) ).
fof(f202,plain,
( x0 = mult(mult(sF0,mult(op_b,op_b)),op_a)
| ~ spl2_1
| ~ spl2_2
| ~ spl2_8 ),
inference(forward_demodulation,[],[f201,f9]) ).
fof(f203,plain,
( x0 = mult(mult(sF1,op_b),op_a)
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5
| ~ spl2_8 ),
inference(forward_demodulation,[],[f202,f72]) ).
fof(f240,plain,
( mult(mult(sF0,mult(op_b,op_b)),op_a) = mult(sF1,mult(op_b,op_a))
| ~ spl2_6
| ~ spl2_8 ),
inference(superposition,[],[f103,f192]) ).
fof(f251,plain,
( mult(mult(sF0,mult(op_b,op_b)),op_a) = mult(sF1,unit)
| ~ spl2_2
| ~ spl2_6
| ~ spl2_8 ),
inference(forward_demodulation,[],[f240,f30]) ).
fof(f253,plain,
( sF1 = mult(mult(sF0,mult(op_b,op_b)),op_a)
| ~ spl2_2
| ~ spl2_6
| ~ spl2_8 ),
inference(forward_demodulation,[],[f251,f9]) ).
fof(f255,plain,
( sF1 = mult(mult(sF1,op_b),op_a)
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8 ),
inference(forward_demodulation,[],[f253,f72]) ).
fof(f257,plain,
( x0 = sF1
| ~ spl2_1
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8 ),
inference(forward_demodulation,[],[f255,f203]) ).
fof(f258,plain,
( $false
| ~ spl2_1
| ~ spl2_2
| spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8 ),
inference(forward_subsumption_resolution,[],[f257,f40]) ).
fof(f259,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8 ),
inference(avatar_contradiction_clause,[],[f258]) ).
cnf(s1,plain,
spl2_1,
inference(sat_conversion,[],[f26]) ).
cnf(s2,plain,
spl2_2,
inference(sat_conversion,[],[f31]) ).
cnf(s3,plain,
spl2_3,
inference(sat_conversion,[],[f36]) ).
cnf(s4,plain,
~ spl2_4,
inference(sat_conversion,[],[f41]) ).
cnf(s5,plain,
spl2_5,
inference(sat_conversion,[],[f51]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_3
| ~ spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
( ~ spl2_3
| spl2_8 ),
inference(sat_conversion,[],[f193]) ).
cnf(s9,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_4
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8 ),
inference(sat_conversion,[],[f259]) ).
cnf(s10,plain,
spl2_8,
inference(rat,[],[s8,s3]) ).
cnf(s12,plain,
~ spl2_6,
inference(rat,[],[s9,s10,s2,s5,s4,s1]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s3,s5,s12,s1]) ).
fof(f260,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP715-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 10:39:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 4.64/1.70 % (3349539)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.64/1.70 % (3349636)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3424505823:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.64/1.70 % (3349637)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1370347853:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.64/1.70 % (3349638)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1541448349:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.64/1.70 % (3349640)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1034146124:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.64/1.70 % (3349639)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1230676629:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.64/1.70 % (3349642)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=204409224:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.64/1.70 % (3349639)Instruction limit reached!
% 4.64/1.70 % (3349639)------------------------------
% 4.64/1.70 % (3349639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.70 % (3349639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.70 % (3349639)CaDiCaL version: 2.1.3
% 4.64/1.70 % (3349639)Termination reason: Instruction limit
% 4.64/1.70 % (3349639)Termination phase: Saturation
% 4.64/1.70 % (3349639)Time elapsed: 0.081 s
% 4.64/1.70 % (3349639)Peak memory usage: 88 MB
% 4.64/1.70 % (3349639)Instructions burned: 137 (million)
% 4.64/1.70 % (3349641)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=204740909:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.64/1.70 % (3349640)Instruction limit reached!
% 4.64/1.70 % (3349640)------------------------------
% 4.64/1.70 % (3349640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.70 % (3349640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.70 % (3349640)CaDiCaL version: 2.1.3
% 4.64/1.70 % (3349640)Termination reason: Instruction limit
% 4.64/1.70 % (3349640)Termination phase: Saturation
% 4.64/1.70 % (3349640)Time elapsed: 0.100 s
% 4.64/1.70 % (3349640)Peak memory usage: 88 MB
% 4.64/1.70 % (3349640)Instructions burned: 182 (million)
% 4.64/1.70 % (3349664)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1244251122:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 4.64/1.70 % (3349663)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2164243683:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 4.64/1.70 % (3349641)Instruction limit reached!
% 4.64/1.70 % (3349641)------------------------------
% 4.64/1.70 % (3349641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.70 % (3349641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.70 % (3349641)CaDiCaL version: 2.1.3
% 4.64/1.70 % (3349641)Termination reason: Instruction limit
% 4.64/1.70 % (3349641)Termination phase: Saturation
% 4.64/1.70 % (3349641)Time elapsed: 0.229 s
% 4.64/1.70 % (3349641)Peak memory usage: 90 MB
% 4.64/1.70 % (3349641)Instructions burned: 259 (million)
% 4.64/1.70 % (3349636)First to succeed.
% 4.64/1.70 % (3349636)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3349539"
% 4.64/1.70 % (3349667)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2879095288:i=215:ep=RSTC_2995 on theBenchmark for (2995ds/215Mi)
% 4.64/1.70 % (3349667)Instruction limit reached!
% 4.64/1.70 % (3349667)------------------------------
% 4.64/1.70 % (3349667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.64/1.70 % (3349667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.64/1.70 % (3349667)CaDiCaL version: 2.1.3
% 6.56/1.91 % (3349667)Termination reason: Instruction limit
% 6.56/1.91 % (3349667)Termination phase: Saturation
% 6.56/1.91 % (3349667)Time elapsed: 0.059 s
% 6.56/1.91 % (3349667)Peak memory usage: 90 MB
% 6.56/1.91 % (3349667)Instructions burned: 216 (million)
% 6.56/1.91 % (3349642)Instruction limit reached!
% 6.56/1.91 % (3349642)------------------------------
% 6.56/1.91 % (3349642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.91 % (3349642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.91 % (3349642)CaDiCaL version: 2.1.3
% 6.56/1.91 % (3349642)Termination reason: Instruction limit
% 6.56/1.91 % (3349642)Termination phase: Saturation
% 6.56/1.91 % (3349642)Time elapsed: 0.643 s
% 6.56/1.91 % (3349642)Peak memory usage: 96 MB
% 6.56/1.91 % (3349642)Instructions burned: 1188 (million)
% 6.56/1.91 % (3349637)Also succeeded, but the first one will report.
% 6.56/1.91 % (3349638)Also succeeded, but the first one will report.
% 6.56/1.91 % (3349636)Refutation found. Thanks to Tanya!
% 6.56/1.91 % SZS status Unsatisfiable for theBenchmark
% 6.56/1.91 % SZS output start Proof for theBenchmark
% See solution above
% 6.56/1.91 % (3349636)------------------------------
% 6.56/1.91 % (3349636)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.56/1.91 % (3349636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.56/1.91 % (3349636)CaDiCaL version: 2.1.3
% 6.56/1.91 % (3349636)Termination reason: Refutation
% 6.56/1.91 % (3349636)Time elapsed: 0.410 s
% 6.56/1.91 % (3349636)Peak memory usage: 129 MB
% 6.56/1.91 % (3349636)Instructions burned: 962 (million)
% 6.56/1.91 % (3349636)------------------------------
% 6.56/1.91 % (3349636)------------------------------
% 6.56/1.91 % (3349539)Success in time 0.835 s
% 6.56/1.91 % Vampire exiting
%------------------------------------------------------------------------------