%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP660-14 : 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 : n004.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 10:15:29 AM UTC 2026
% Result : Unsatisfiable 6.35s 1.94s
% Output : Refutation 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 74 unt; 6 def)
% Number of atoms : 74 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 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 : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 67 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,negated_conjecture,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,negated_conjecture,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,negated_conjecture,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
mult(ld(x1,x1),x0) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f7,plain,
x0 != mult(ld(x1,x1),x0),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
! [X0,X1] : sF0(X0,X1) = mult(X0,ld(X0,X1)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = sF0(X0,X1),
inference(reorient_equations,[],[f8]) ).
fof(f10,plain,
! [X0,X1] : sF0(X0,X1) = X1,
inference(definition_folding,[],[f1,f9]) ).
fof(f11,definition,
! [X0,X1] : sF1(X0,X1) = ld(X0,mult(X0,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f12,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = sF1(X0,X1),
inference(reorient_equations,[],[f11]) ).
fof(f13,plain,
! [X0,X1] : sF1(X0,X1) = X1,
inference(definition_folding,[],[f2,f12]) ).
fof(f14,definition,
! [X0,X1] : sF2(X0,X1) = mult(rd(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f15,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = sF2(X0,X1),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X0,X1] : sF2(X0,X1) = X0,
inference(definition_folding,[],[f3,f15]) ).
fof(f17,definition,
! [X0,X1] : sF3(X0,X1) = rd(mult(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f18,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = sF3(X0,X1),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : sF3(X0,X1) = X0,
inference(definition_folding,[],[f4,f18]) ).
fof(f20,definition,
sF4 = ld(x1,x1),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f21,plain,
ld(x1,x1) = sF4,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF5 = mult(sF4,x0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f23,plain,
mult(sF4,x0) = sF5,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
x0 != sF5,
inference(definition_folding,[],[f7,f23,f21]) ).
fof(f25,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f19,f18]) ).
fof(f26,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f16,f15]) ).
fof(f27,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(forward_demodulation,[],[f13,f12]) ).
fof(f28,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(forward_demodulation,[],[f10,f9]) ).
fof(f30,plain,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = rd(mult(X0,mult(X1,mult(X2,X0))),X0),
inference(superposition,[],[f25,f5]) ).
fof(f33,plain,
x0 = ld(sF4,sF5),
inference(superposition,[],[f27,f23]) ).
fof(f34,plain,
! [X2,X0,X1] : ld(mult(mult(X0,X1),X2),mult(X0,mult(X1,mult(X2,X0)))) = X0,
inference(superposition,[],[f27,f5]) ).
fof(f36,plain,
x1 = mult(x1,sF4),
inference(superposition,[],[f28,f21]) ).
fof(f38,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(superposition,[],[f25,f28]) ).
fof(f39,plain,
! [X2,X0,X1] : mult(X1,mult(ld(X1,X0),mult(X2,X1))) = mult(mult(X0,X2),X1),
inference(superposition,[],[f5,f28]) ).
fof(f40,plain,
! [X2,X0,X1] : mult(X0,X1) = mult(X1,mult(X2,mult(ld(mult(X1,X2),X0),X1))),
inference(superposition,[],[f5,f28]) ).
fof(f42,plain,
x1 = rd(x1,sF4),
inference(superposition,[],[f25,f36]) ).
fof(f43,plain,
! [X0] : mult(x1,mult(sF4,mult(X0,x1))) = mult(mult(x1,X0),x1),
inference(superposition,[],[f5,f36]) ).
fof(f53,plain,
mult(x1,mult(sF4,mult(sF4,x1))) = mult(x1,x1),
inference(superposition,[],[f43,f36]) ).
fof(f61,plain,
mult(sF4,mult(sF4,x1)) = ld(x1,mult(x1,x1)),
inference(superposition,[],[f27,f53]) ).
fof(f65,plain,
x1 = mult(sF4,mult(sF4,x1)),
inference(forward_demodulation,[],[f61,f27]) ).
fof(f77,plain,
! [X2,X0,X1] : mult(mult(X1,X2),rd(X0,X1)) = rd(mult(X1,mult(X2,X0)),X1),
inference(superposition,[],[f30,f26]) ).
fof(f78,plain,
! [X0] : mult(mult(sF4,X0),x1) = rd(mult(sF4,mult(X0,x1)),sF4),
inference(superposition,[],[f30,f36]) ).
fof(f100,plain,
! [X0] : mult(mult(sF4,rd(X0,x1)),x1) = rd(mult(sF4,X0),sF4),
inference(superposition,[],[f78,f26]) ).
fof(f101,plain,
rd(x1,sF4) = mult(mult(sF4,sF4),x1),
inference(superposition,[],[f78,f65]) ).
fof(f105,plain,
x1 = mult(mult(sF4,sF4),x1),
inference(forward_demodulation,[],[f101,f42]) ).
fof(f110,plain,
mult(sF4,sF4) = rd(x1,x1),
inference(superposition,[],[f25,f105]) ).
fof(f158,plain,
sF4 = mult(mult(sF4,rd(sF4,x1)),x1),
inference(superposition,[],[f100,f25]) ).
fof(f199,plain,
! [X2,X0,X1] : ld(mult(mult(X1,X2),rd(X0,X1)),mult(X1,mult(X2,X0))) = X1,
inference(superposition,[],[f34,f26]) ).
fof(f363,plain,
sF4 = mult(x1,mult(ld(x1,sF4),mult(rd(sF4,x1),x1))),
inference(superposition,[],[f158,f39]) ).
fof(f384,plain,
sF4 = mult(x1,mult(ld(x1,sF4),sF4)),
inference(forward_demodulation,[],[f363,f26]) ).
fof(f401,plain,
rd(mult(sF4,sF4),sF4) = mult(mult(sF4,x1),ld(x1,sF4)),
inference(superposition,[],[f30,f384]) ).
fof(f410,plain,
sF4 = mult(mult(sF4,x1),ld(x1,sF4)),
inference(forward_demodulation,[],[f401,f25]) ).
fof(f429,plain,
mult(sF4,x1) = rd(sF4,ld(x1,sF4)),
inference(superposition,[],[f25,f410]) ).
fof(f436,plain,
x1 = mult(sF4,x1),
inference(forward_demodulation,[],[f429,f38]) ).
fof(f448,plain,
sF4 = rd(x1,x1),
inference(superposition,[],[f25,f436]) ).
fof(f455,plain,
sF4 = mult(sF4,sF4),
inference(forward_demodulation,[],[f448,f110]) ).
fof(f474,plain,
sF4 = rd(sF4,sF4),
inference(superposition,[],[f25,f455]) ).
fof(f2652,plain,
! [X0] : ld(mult(mult(X0,sF4),rd(x0,X0)),mult(X0,sF5)) = X0,
inference(superposition,[],[f199,f23]) ).
fof(f2809,plain,
sF4 = ld(mult(sF4,rd(x0,sF4)),mult(sF4,sF5)),
inference(superposition,[],[f2652,f455]) ).
fof(f2826,plain,
mult(mult(sF4,sF5),sF4) = mult(sF4,mult(rd(x0,sF4),mult(sF4,sF4))),
inference(superposition,[],[f40,f2809]) ).
fof(f2833,plain,
mult(mult(sF4,sF5),sF4) = mult(sF4,mult(rd(x0,sF4),sF4)),
inference(forward_demodulation,[],[f2826,f455]) ).
fof(f2835,plain,
mult(sF4,x0) = mult(mult(sF4,sF5),sF4),
inference(forward_demodulation,[],[f2833,f26]) ).
fof(f2837,plain,
sF5 = mult(mult(sF4,sF5),sF4),
inference(forward_demodulation,[],[f2835,f23]) ).
fof(f2839,plain,
mult(sF5,sF4) = mult(sF4,mult(sF5,mult(sF4,sF4))),
inference(superposition,[],[f5,f2837]) ).
fof(f2869,plain,
mult(sF5,sF4) = mult(sF4,mult(sF5,sF4)),
inference(forward_demodulation,[],[f2839,f455]) ).
fof(f2897,plain,
rd(mult(sF4,mult(sF5,sF4)),sF4) = mult(mult(sF4,sF4),sF5),
inference(superposition,[],[f30,f2869]) ).
fof(f2914,plain,
mult(sF4,sF5) = rd(mult(sF4,mult(sF5,sF4)),sF4),
inference(forward_demodulation,[],[f2897,f455]) ).
fof(f2920,plain,
mult(sF4,sF5) = mult(mult(sF4,sF5),rd(sF4,sF4)),
inference(forward_demodulation,[],[f2914,f77]) ).
fof(f2925,plain,
mult(sF4,sF5) = mult(mult(sF4,sF5),sF4),
inference(forward_demodulation,[],[f2920,f474]) ).
fof(f2927,plain,
sF5 = mult(sF4,sF5),
inference(forward_demodulation,[],[f2925,f2837]) ).
fof(f2942,plain,
sF5 = ld(sF4,sF5),
inference(superposition,[],[f27,f2927]) ).
fof(f2958,plain,
x0 = sF5,
inference(forward_demodulation,[],[f2942,f33]) ).
fof(f2974,plain,
x0 != x0,
inference(superposition,[],[f24,f2958]) ).
fof(f3025,plain,
$false,
inference(trivial_inequality_removal,[],[f2974]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660-14 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 10:32:52 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 6.35/1.94 % (3315679)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.35/1.94 % (3315702)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=705233928:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.35/1.94 % (3315698)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=1842829050:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.35/1.94 % (3315700)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1556760818:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.35/1.94 % (3315697)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=4129705303:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.35/1.94 % (3315699)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3812015193:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.35/1.94 % (3315702)Instruction limit reached!
% 6.35/1.94 % (3315702)------------------------------
% 6.35/1.94 % (3315702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.35/1.94 % (3315702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.94 % (3315702)CaDiCaL version: 2.1.3
% 6.35/1.94 % (3315702)Termination reason: Instruction limit
% 6.35/1.94 % (3315702)Termination phase: Saturation
% 6.35/1.94 % (3315702)Time elapsed: 0.079 s
% 6.35/1.94 % (3315702)Peak memory usage: 91 MB
% 6.35/1.94 % (3315702)Instructions burned: 258 (million)
% 6.35/1.94 % (3315703)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1457688520:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.35/1.94 % (3315701)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1763508878:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.35/1.94 % (3315700)Instruction limit reached!
% 6.35/1.94 % (3315700)------------------------------
% 6.35/1.94 % (3315700)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.35/1.94 % (3315700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.94 % (3315700)CaDiCaL version: 2.1.3
% 6.35/1.94 % (3315700)Termination reason: Instruction limit
% 6.35/1.94 % (3315700)Termination phase: Saturation
% 6.35/1.94 % (3315700)Time elapsed: 0.130 s
% 6.35/1.94 % (3315700)Peak memory usage: 88 MB
% 6.35/1.94 % (3315700)Instructions burned: 136 (million)
% 6.35/1.94 % (3315701)First to succeed.
% 6.35/1.94 % (3315701)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3315679"
% 6.35/1.94 % (3315718)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1838994214:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.35/1.94 % (3315727)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3489322984:i=4948:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/4948Mi)
% 6.35/1.94 % (3315701)Refutation found. Thanks to Tanya!
% 6.35/1.94 % SZS status Unsatisfiable for theBenchmark
% 6.35/1.94 % SZS output start Proof for theBenchmark
% See solution above
% 6.35/1.94 % (3315701)------------------------------
% 6.35/1.94 % (3315701)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.35/1.94 % (3315701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.94 % (3315701)CaDiCaL version: 2.1.3
% 6.35/1.94 % (3315701)Termination reason: Refutation
% 6.35/1.94 % (3315701)Time elapsed: 0.127 s
% 6.35/1.94 % (3315701)Peak memory usage: 90 MB
% 6.35/1.94 % (3315701)Instructions burned: 127 (million)
% 6.35/1.94 % (3315701)------------------------------
% 6.35/1.94 % (3315701)------------------------------
% 6.35/1.94 % (3315679)Success in time 0.802 s
% 6.35/1.94 % Vampire exiting
%------------------------------------------------------------------------------