%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP700-10 : 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 : n012.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 10:15:58 AM UTC 2026
% Result : Unsatisfiable 3.16s 1.19s
% Output : Refutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 62 ( 62 unt; 10 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 87 !; 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,negated_conjecture,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f8,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X1,mult(X2,X1))) = mult(mult(X0,mult(X1,mult(X1,X2))),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(f9,negated_conjecture,
! [X0] : tuple(mult(X0,x0),mult(x0,X0)) != tuple(unit,unit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f10,definition,
! [X0,X1] : sF0(X0,X1) = mult(X0,ld(X0,X1)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f11,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = sF0(X0,X1),
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
! [X0,X1] : sF0(X0,X1) = X1,
inference(definition_folding,[],[f1,f11]) ).
fof(f13,definition,
! [X0,X1] : sF1(X0,X1) = ld(X0,mult(X0,X1)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f14,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = sF1(X0,X1),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X0,X1] : sF1(X0,X1) = X1,
inference(definition_folding,[],[f2,f14]) ).
fof(f16,definition,
! [X0,X1] : sF2(X0,X1) = mult(rd(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f17,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = sF2(X0,X1),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0,X1] : sF2(X0,X1) = X0,
inference(definition_folding,[],[f3,f17]) ).
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(f22,definition,
! [X0] : sF4(X0) = mult(X0,unit),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f23,plain,
! [X0] : mult(X0,unit) = sF4(X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] : sF4(X0) = X0,
inference(definition_folding,[],[f5,f23]) ).
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(X0,x0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f29,plain,
! [X0] : mult(X0,x0) = sF6(X0),
inference(reorient_equations,[],[f28]) ).
fof(f30,definition,
! [X0] : sF7(X0) = mult(x0,X0),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f31,plain,
! [X0] : mult(x0,X0) = sF7(X0),
inference(reorient_equations,[],[f30]) ).
fof(f32,definition,
! [X0] : sF8(X0) = tuple(sF6(X0),sF7(X0)),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f33,plain,
! [X0] : tuple(sF6(X0),sF7(X0)) = sF8(X0),
inference(reorient_equations,[],[f32]) ).
fof(f34,definition,
sF9 = tuple(unit,unit),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f35,plain,
tuple(unit,unit) = sF9,
inference(reorient_equations,[],[f34]) ).
fof(f36,plain,
! [X0] : sF8(X0) != sF9,
inference(definition_folding,[],[f9,f35,f33,f31,f29]) ).
fof(f37,plain,
! [X0] : tuple(sF6(X0),sF7(X0)) != sF9,
inference(forward_demodulation,[],[f36,f33]) ).
fof(f38,plain,
! [X0] : mult(unit,X0) = X0,
inference(forward_demodulation,[],[f27,f26]) ).
fof(f39,plain,
! [X0] : mult(X0,unit) = X0,
inference(forward_demodulation,[],[f24,f23]) ).
fof(f40,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f21,f20]) ).
fof(f41,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f18,f17]) ).
fof(f42,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f43,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(forward_demodulation,[],[f12,f11]) ).
fof(f44,plain,
! [X0] : sF9 != tuple(sF6(X0),mult(x0,X0)),
inference(forward_demodulation,[],[f37,f31]) ).
fof(f45,plain,
! [X0] : tuple(mult(X0,x0),mult(x0,X0)) != sF9,
inference(forward_demodulation,[],[f44,f29]) ).
fof(f53,plain,
! [X0,X1] : mult(mult(unit,X0),mult(X0,mult(X1,X0))) = mult(mult(X0,mult(X0,X1)),X0),
inference(superposition,[],[f8,f38]) ).
fof(f54,plain,
! [X0,X1] : mult(mult(X0,mult(X0,X1)),X0) = mult(X0,mult(X0,mult(X1,X0))),
inference(forward_demodulation,[],[f53,f38]) ).
fof(f68,plain,
! [X0,X1] : mult(mult(X1,X0),mult(X0,mult(unit,X0))) = mult(mult(X1,mult(X0,X0)),X0),
inference(superposition,[],[f8,f39]) ).
fof(f83,plain,
! [X0,X1] : mult(mult(X1,mult(X0,X0)),X0) = mult(mult(X1,X0),mult(X0,X0)),
inference(forward_demodulation,[],[f68,f38]) ).
fof(f118,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[],[f42,f41]) ).
fof(f121,plain,
! [X0] : unit = ld(X0,X0),
inference(superposition,[],[f42,f39]) ).
fof(f143,plain,
! [X0] : sF9 != tuple(mult(ld(x0,X0),x0),X0),
inference(superposition,[],[f45,f43]) ).
fof(f166,plain,
! [X0,X1] : mult(mult(X1,X0),X1) = mult(X1,mult(X1,mult(ld(X1,X0),X1))),
inference(superposition,[],[f54,f43]) ).
fof(f362,plain,
! [X0,X1] : ld(mult(X0,mult(X1,X1)),mult(mult(X0,X1),mult(X1,X1))) = X1,
inference(superposition,[],[f42,f83]) ).
fof(f419,plain,
! [X0,X1] : rd(mult(mult(X0,X1),X0),mult(X0,mult(ld(X0,X1),X0))) = X0,
inference(superposition,[],[f40,f166]) ).
fof(f1109,plain,
! [X0] : rd(mult(X0,X0),mult(X0,mult(ld(X0,unit),X0))) = X0,
inference(superposition,[],[f419,f39]) ).
fof(f1171,plain,
! [X0] : mult(X0,mult(ld(X0,unit),X0)) = ld(X0,mult(X0,X0)),
inference(superposition,[],[f118,f1109]) ).
fof(f1174,plain,
! [X0] : mult(X0,mult(ld(X0,unit),X0)) = X0,
inference(forward_demodulation,[],[f1171,f42]) ).
fof(f1210,plain,
! [X0] : mult(ld(X0,unit),X0) = ld(mult(X0,mult(mult(ld(X0,unit),X0),mult(ld(X0,unit),X0))),mult(X0,mult(mult(ld(X0,unit),X0),mult(ld(X0,unit),X0)))),
inference(superposition,[],[f362,f1174]) ).
fof(f1219,plain,
! [X0] : unit = mult(ld(X0,unit),X0),
inference(forward_demodulation,[],[f1210,f121]) ).
fof(f1250,plain,
tuple(unit,unit) != sF9,
inference(superposition,[],[f143,f1219]) ).
fof(f1303,plain,
sF9 != sF9,
inference(forward_demodulation,[],[f1250,f35]) ).
fof(f1304,plain,
$false,
inference(trivial_inequality_removal,[],[f1303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP700-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Sun Sep 27 10:36:05 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.33 Running first-order theorem proving
% 0.07/0.33 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
% 3.16/1.19 % (2183239)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.16/1.19 % (2183288)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3017898968:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.16/1.19 % (2183289)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=573655853:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.16/1.19 % (2183283)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=4190659751:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.16/1.19 % (2183284)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=907214463:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.16/1.19 % (2183286)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2594742889:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.16/1.19 % (2183287)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4136645113:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.16/1.19 % (2183285)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3189864619:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.16/1.19 % (2183287)First to succeed.
% 3.16/1.19 % (2183287)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2183239"
% 3.16/1.19 % (2183286)Instruction limit reached!
% 3.16/1.19 % (2183286)------------------------------
% 3.16/1.19 % (2183286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.19 % (2183286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.19 % (2183286)CaDiCaL version: 2.1.3
% 3.16/1.19 % (2183286)Termination reason: Instruction limit
% 3.16/1.19 % (2183286)Termination phase: Saturation
% 3.16/1.19 % (2183286)Time elapsed: 0.046 s
% 3.16/1.19 % (2183286)Peak memory usage: 89 MB
% 3.16/1.19 % (2183286)Instructions burned: 138 (million)
% 3.16/1.19 % (2183288)Instruction limit reached!
% 3.16/1.19 % (2183288)------------------------------
% 3.16/1.19 % (2183288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.19 % (2183288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.19 % (2183288)CaDiCaL version: 2.1.3
% 3.16/1.19 % (2183288)Termination reason: Instruction limit
% 3.16/1.19 % (2183288)Termination phase: Saturation
% 3.16/1.19 % (2183288)Time elapsed: 0.142 s
% 3.16/1.19 % (2183288)Peak memory usage: 90 MB
% 3.16/1.19 % (2183288)Instructions burned: 259 (million)
% 3.16/1.19 % (2183303)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3257194601:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 3.16/1.19 % (2183287)Refutation found. Thanks to Tanya!
% 3.16/1.19 % SZS status Unsatisfiable for theBenchmark
% 3.16/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.16/1.19 % (2183287)------------------------------
% 3.16/1.19 % (2183287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.16/1.19 % (2183287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.16/1.19 % (2183287)CaDiCaL version: 2.1.3
% 3.16/1.19 % (2183287)Termination reason: Refutation
% 3.16/1.19 % (2183287)Time elapsed: 0.026 s
% 3.16/1.19 % (2183287)Peak memory usage: 88 MB
% 3.16/1.19 % (2183287)Instructions burned: 50 (million)
% 3.16/1.19 % (2183287)------------------------------
% 3.16/1.19 % (2183287)------------------------------
% 3.16/1.19 % (2183239)Success in time 0.399 s
% 3.16/1.19 % Vampire exiting
%------------------------------------------------------------------------------