%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP679-1 : 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 : n015.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 10:15:34 AM UTC 2026
% Result : Unsatisfiable 0.15s 1.50s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 40 unt; 7 def)
% Number of atoms : 40 ( 39 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,negated_conjecture,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
fof(f6,negated_conjecture,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
fof(f7,axiom,
! [X2,X0,X1] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(X0,mult(X1,X0)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
fof(f8,negated_conjecture,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
fof(f9,negated_conjecture,
mult(mult(op_c,op_c),a) != mult(a,mult(op_c,op_c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f19,definition,
! [X0,X1] : sF3(X0,X1) = rd(mult(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f20,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = sF3(X0,X1),
inference(reorient_equations,[],[f19]) ).
fof(f21,plain,
! [X0,X1] : sF3(X0,X1) = X0,
inference(definition_folding,[],[f4,f20]) ).
fof(f25,definition,
! [X0] : sF5(X0) = mult(unit,X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f26,plain,
! [X0] : mult(unit,X0) = sF5(X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : sF5(X0) = X0,
inference(definition_folding,[],[f6,f26]) ).
fof(f28,definition,
! [X0] : sF6(X0) = mult(op_c,X0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f29,plain,
! [X0] : mult(op_c,X0) = sF6(X0),
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
! [X0] : sF7(X0) = mult(X0,op_c),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f31,plain,
! [X0] : mult(X0,op_c) = sF7(X0),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
! [X0] : sF6(X0) = sF7(X0),
inference(definition_folding,[],[f8,f31,f29]) ).
fof(f33,definition,
sF8 = mult(op_c,op_c),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f34,plain,
mult(op_c,op_c) = sF8,
inference(reorient_equations,[],[f33]) ).
fof(f35,definition,
sF9 = mult(sF8,a),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f36,plain,
mult(sF8,a) = sF9,
inference(reorient_equations,[],[f35]) ).
fof(f37,definition,
sF10 = mult(a,sF8),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f38,plain,
mult(a,sF8) = sF10,
inference(reorient_equations,[],[f37]) ).
fof(f39,plain,
sF9 != sF10,
inference(definition_folding,[],[f9,f38,f34,f36,f34]) ).
fof(f40,plain,
! [X0] : mult(X0,op_c) = sF6(X0),
inference(forward_demodulation,[],[f32,f31]) ).
fof(f41,plain,
! [X0] : mult(unit,X0) = X0,
inference(forward_demodulation,[],[f27,f26]) ).
fof(f43,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f47,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(forward_demodulation,[],[f40,f29]) ).
fof(f48,plain,
! [X0,X1] : mult(X0,mult(unit,mult(X0,X1))) = mult(mult(X0,X0),X1),
inference(superposition,[],[f7,f41]) ).
fof(f51,plain,
! [X0,X1] : mult(mult(X0,X0),X1) = mult(X0,mult(X0,X1)),
inference(forward_demodulation,[],[f48,f41]) ).
fof(f59,plain,
! [X2,X0,X1] : mult(X0,mult(X1,X0)) = rd(mult(X0,mult(X1,mult(X0,X2))),X2),
inference(superposition,[],[f43,f7]) ).
fof(f101,plain,
! [X0] : rd(mult(op_c,X0),op_c) = X0,
inference(superposition,[],[f43,f47]) ).
fof(f185,plain,
! [X0] : mult(op_c,mult(op_c,X0)) = mult(sF8,X0),
inference(superposition,[],[f51,f34]) ).
fof(f205,plain,
sF9 = mult(op_c,mult(op_c,a)),
inference(superposition,[],[f185,f36]) ).
fof(f271,plain,
! [X0] : mult(op_c,mult(X0,op_c)) = mult(X0,mult(op_c,op_c)),
inference(superposition,[],[f101,f59]) ).
fof(f277,plain,
! [X0] : mult(op_c,mult(X0,op_c)) = mult(X0,sF8),
inference(forward_demodulation,[],[f271,f34]) ).
fof(f331,plain,
sF10 = mult(op_c,mult(a,op_c)),
inference(superposition,[],[f38,f277]) ).
fof(f334,plain,
sF10 = mult(op_c,mult(op_c,a)),
inference(forward_demodulation,[],[f331,f47]) ).
fof(f349,plain,
sF9 = sF10,
inference(forward_demodulation,[],[f334,f205]) ).
fof(f357,plain,
sF9 != sF9,
inference(superposition,[],[f39,f349]) ).
fof(f358,plain,
$false,
inference(trivial_inequality_removal,[],[f357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP679-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n015.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 10:38:45 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.15/1.50 % (1460047)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.15/1.50 % (1460055)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1590958146:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.15/1.50 % (1460055)Instruction limit reached!
% 0.15/1.50 % (1460055)------------------------------
% 0.15/1.50 % (1460055)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1460055)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1460055)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1460055)Termination reason: Instruction limit
% 0.15/1.50 % (1460055)Termination phase: Saturation
% 0.15/1.50 % (1460055)Time elapsed: 0.042 s
% 0.15/1.50 % (1460055)Peak memory usage: 89 MB
% 0.15/1.50 % (1460055)Instructions burned: 139 (million)
% 0.15/1.50 % (1460058)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2106932431:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.15/1.50 % (1460056)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=911110427:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.15/1.50 % (1460054)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3190892338:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.15/1.50 % (1460053)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=1007926285:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.15/1.50 % (1460052)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=1993474900:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.15/1.50 % (1460057)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=730121718:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.15/1.50 % (1460056)First to succeed.
% 0.15/1.50 % (1460056)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1460047"
% 0.15/1.50 % (1460058)Also succeeded, but the first one will report.
% 0.15/1.50 % (1460060)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1250353580:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 0.15/1.50 % (1460057)Instruction limit reached!
% 0.15/1.50 % (1460057)------------------------------
% 0.15/1.50 % (1460057)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1460057)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1460057)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1460057)Termination reason: Instruction limit
% 0.15/1.50 % (1460057)Termination phase: Saturation
% 0.15/1.50 % (1460057)Time elapsed: 0.140 s
% 0.15/1.50 % (1460057)Peak memory usage: 90 MB
% 0.15/1.50 % (1460057)Instructions burned: 259 (million)
% 0.15/1.50 % (1460056)Refutation found. Thanks to Tanya!
% 0.15/1.50 % SZS status Unsatisfiable for theBenchmark
% 0.15/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (1460056)------------------------------
% 0.15/1.50 % (1460056)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (1460056)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (1460056)CaDiCaL version: 2.1.3
% 0.15/1.50 % (1460056)Termination reason: Refutation
% 0.15/1.50 % (1460056)Time elapsed: 0.010 s
% 0.15/1.50 % (1460056)Peak memory usage: 88 MB
% 0.15/1.50 % (1460056)Instructions burned: 14 (million)
% 0.15/1.50 % (1460056)------------------------------
% 0.15/1.50 % (1460056)------------------------------
% 0.15/1.50 % (1460047)Success in time 0.447 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------