%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 10:15:27 AM UTC 2026
% Result : Unsatisfiable 2.64s 1.24s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 52 ( 52 unt; 7 def)
% Number of atoms : 52 ( 51 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 : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 0 con; 1-2 aty)
% Number of variables : 97 ( 97 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f3,negated_conjecture,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,negated_conjecture,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(mult(X0,mult(X1,X1)),X2) = mult(mult(X0,X1),mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
fof(f7,definition,
! [X0,X1] : sF0(X0,X1) = mult(X0,ld(X0,X1)),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f8,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = sF0(X0,X1),
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
! [X0,X1] : sF0(X0,X1) = X1,
inference(definition_folding,[],[f1,f8]) ).
fof(f13,definition,
! [X0,X1] : sF2(X0,X1) = mult(rd(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f14,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = sF2(X0,X1),
inference(reorient_equations,[],[f13]) ).
fof(f15,plain,
! [X0,X1] : sF2(X0,X1) = X0,
inference(definition_folding,[],[f3,f14]) ).
fof(f16,definition,
! [X0,X1] : sF3(X0,X1) = rd(mult(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f17,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = sF3(X0,X1),
inference(reorient_equations,[],[f16]) ).
fof(f18,plain,
! [X0,X1] : sF3(X0,X1) = X0,
inference(definition_folding,[],[f4,f17]) ).
fof(f19,definition,
! [X0] : sF4(X0) = mult(X0,x1(X0)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f20,plain,
! [X0] : mult(X0,x1(X0)) = sF4(X0),
inference(reorient_equations,[],[f19]) ).
fof(f21,definition,
! [X0] : sF5(X0) = mult(x1_2(X0),X0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f22,plain,
! [X0] : mult(x1_2(X0),X0) = sF5(X0),
inference(reorient_equations,[],[f21]) ).
fof(f23,definition,
! [X0] : sF6(X0) = tuple(sF4(X0),sF5(X0)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f24,plain,
! [X0] : tuple(sF4(X0),sF5(X0)) = sF6(X0),
inference(reorient_equations,[],[f23]) ).
fof(f25,definition,
! [X0] : sF7(X0) = tuple(x1(X0),x1_2(X0)),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f26,plain,
! [X0] : tuple(x1(X0),x1_2(X0)) = sF7(X0),
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
! [X0] : sF6(X0) != sF7(X0),
inference(definition_folding,[],[f6,f26,f24,f22,f20]) ).
fof(f28,plain,
! [X0] : tuple(x1(X0),x1_2(X0)) != sF6(X0),
inference(forward_demodulation,[],[f27,f26]) ).
fof(f29,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f18,f17]) ).
fof(f30,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(forward_demodulation,[],[f15,f14]) ).
fof(f32,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(forward_demodulation,[],[f9,f8]) ).
fof(f33,plain,
! [X0] : tuple(x1(X0),x1_2(X0)) != tuple(sF4(X0),sF5(X0)),
inference(forward_demodulation,[],[f28,f24]) ).
fof(f34,plain,
! [X0] : tuple(x1(X0),x1_2(X0)) != tuple(sF4(X0),mult(x1_2(X0),X0)),
inference(forward_demodulation,[],[f33,f22]) ).
fof(f35,plain,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
inference(forward_demodulation,[],[f34,f20]) ).
fof(f36,plain,
! [X2,X0,X1] : mult(X0,mult(X1,X1)) = rd(mult(mult(X0,X1),mult(X1,X2)),X2),
inference(superposition,[],[f29,f5]) ).
fof(f37,plain,
! [X2,X0,X1] : mult(mult(rd(X0,mult(X1,X1)),X1),mult(X1,X2)) = mult(X0,X2),
inference(superposition,[],[f5,f30]) ).
fof(f49,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(X1,X1)) = rd(mult(X0,mult(X1,X2)),X2),
inference(superposition,[],[f36,f30]) ).
fof(f65,plain,
! [X2,X0,X1] : mult(X1,ld(X2,X0)) = mult(mult(rd(X1,mult(X2,X2)),X2),X0),
inference(superposition,[],[f37,f32]) ).
fof(f73,plain,
! [X2,X0,X1] : mult(rd(X0,mult(X2,X2)),X2) = rd(mult(X0,X1),mult(X2,X1)),
inference(superposition,[],[f29,f37]) ).
fof(f175,plain,
! [X0,X1] : mult(mult(rd(X1,mult(X1,X1)),X1),X0) = X0,
inference(superposition,[],[f65,f32]) ).
fof(f274,plain,
! [X0,X1] : mult(rd(X1,mult(X1,X1)),X1) = rd(X0,X0),
inference(superposition,[],[f29,f175]) ).
fof(f341,plain,
! [X2,X0] : rd(X0,X0) = rd(X2,X2),
inference(superposition,[],[f274,f274]) ).
fof(f346,plain,
! [X2,X0] : mult(rd(X0,X0),X2) = X2,
inference(superposition,[],[f175,f274]) ).
fof(f349,plain,
! [X2,X0,X1] : mult(rd(X1,mult(X1,X1)),mult(X1,X1)) = rd(mult(rd(X0,X0),mult(X1,X2)),X2),
inference(superposition,[],[f36,f274]) ).
fof(f373,plain,
! [X0,X1] : mult(rd(X1,mult(X1,X1)),mult(X1,X1)) = mult(rd(rd(X0,X0),X1),mult(X1,X1)),
inference(forward_demodulation,[],[f349,f49]) ).
fof(f377,plain,
! [X0,X1] : mult(rd(rd(X0,X0),X1),mult(X1,X1)) = X1,
inference(forward_demodulation,[],[f373,f30]) ).
fof(f802,plain,
! [X2,X0,X1] : mult(rd(rd(X0,X1),mult(X2,X2)),X2) = rd(X0,mult(X2,X1)),
inference(superposition,[],[f73,f30]) ).
fof(f3041,plain,
! [X2,X0,X1] : rd(X1,mult(X2,X1)) = mult(rd(rd(X0,X0),mult(X2,X2)),X2),
inference(superposition,[],[f802,f341]) ).
fof(f3143,plain,
! [X2,X0,X1] : rd(X0,mult(X2,X0)) = rd(X1,mult(X2,X1)),
inference(forward_demodulation,[],[f3041,f802]) ).
fof(f3163,plain,
! [X2,X0,X1] : rd(X1,X0) = rd(X2,mult(rd(X0,X1),X2)),
inference(superposition,[],[f3143,f30]) ).
fof(f3344,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = rd(mult(X0,X0),X0),
inference(superposition,[],[f3163,f377]) ).
fof(f3435,plain,
! [X0,X1] : rd(X0,rd(X1,X1)) = X0,
inference(forward_demodulation,[],[f3344,f29]) ).
fof(f3475,plain,
! [X0,X1] : mult(X0,rd(X1,X1)) = X0,
inference(superposition,[],[f3435,f29]) ).
fof(f3642,plain,
! [X0] : tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))) != tuple(mult(rd(X0,X0),x1(rd(X0,X0))),x1_2(rd(X0,X0))),
inference(superposition,[],[f35,f3475]) ).
fof(f3643,plain,
! [X0] : tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))) != tuple(x1(rd(X0,X0)),x1_2(rd(X0,X0))),
inference(forward_demodulation,[],[f3642,f346]) ).
fof(f3644,plain,
$false,
inference(trivial_inequality_removal,[],[f3643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n006.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 10:32:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.64/1.24 % (2779841)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.64/1.24 % (2779850)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=22090731:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.64/1.24 % (2779848)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2018966848:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.64/1.24 % (2779851)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2875449239:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.64/1.24 % (2779849)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3745152010:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.64/1.24 % (2779847)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=2075183466:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.64/1.24 % (2779846)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=1218339986:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.64/1.24 % (2779850)First to succeed.
% 2.64/1.24 % (2779852)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1660259082:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.64/1.24 % (2779850)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2779841"
% 2.64/1.24 % (2779849)Instruction limit reached!
% 2.64/1.24 % (2779849)------------------------------
% 2.64/1.24 % (2779849)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (2779849)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (2779849)CaDiCaL version: 2.1.3
% 2.64/1.24 % (2779849)Termination reason: Instruction limit
% 2.64/1.24 % (2779849)Termination phase: Saturation
% 2.64/1.24 % (2779849)Time elapsed: 0.076 s
% 2.64/1.24 % (2779849)Peak memory usage: 89 MB
% 2.64/1.24 % (2779849)Instructions burned: 136 (million)
% 2.64/1.24 % (2779850)Refutation found. Thanks to Tanya!
% 2.64/1.24 % SZS status Unsatisfiable for theBenchmark
% 2.64/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.24 % (2779850)------------------------------
% 2.64/1.24 % (2779850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.24 % (2779850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.24 % (2779850)CaDiCaL version: 2.1.3
% 2.64/1.24 % (2779850)Termination reason: Refutation
% 2.64/1.24 % (2779850)Time elapsed: 0.046 s
% 2.64/1.24 % (2779850)Peak memory usage: 89 MB
% 2.64/1.24 % (2779850)Instructions burned: 137 (million)
% 2.64/1.24 % (2779850)------------------------------
% 2.64/1.24 % (2779850)------------------------------
% 2.64/1.24 % (2779841)Success in time 0.304 s
% 2.64/1.24 % Vampire exiting
%------------------------------------------------------------------------------