%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 10:13:59 AM UTC 2026
% Result : Unsatisfiable 3.14s 1.13s
% Output : Refutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 79 unt; 11 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-4 aty)
% Number of variables : 120 ( 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_1) ).
fof(f3,definition,
! [X2,X0,X1] : sF0(X0,X1,X2) = multiply(multiply(X0,X1),X2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f4,plain,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = sF0(X0,X1,X2),
inference(reorient_equations,[],[f3]) ).
fof(f5,definition,
! [X2,X0,X1] : sF1(X0,X1,X2) = inverse(sF0(X0,X1,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f6,plain,
! [X2,X0,X1] : inverse(sF0(X0,X1,X2)) = sF1(X0,X1,X2),
inference(reorient_equations,[],[f5]) ).
fof(f7,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = multiply(sF1(X0,X1,X2),X0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f8,plain,
! [X2,X0,X1] : multiply(sF1(X0,X1,X2),X0) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X2,X0,X1] : sF3(X0,X1,X2) = multiply(sF2(X0,X1,X2),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f10,plain,
! [X2,X0,X1] : multiply(sF2(X0,X1,X2),X1) = sF3(X0,X1,X2),
inference(reorient_equations,[],[f9]) ).
fof(f11,definition,
! [X3] : sF4(X3) = multiply(X3,inverse(X3)),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f12,plain,
! [X3] : multiply(X3,inverse(X3)) = sF4(X3),
inference(reorient_equations,[],[f11]) ).
fof(f13,definition,
! [X2,X3,X0,X1] : sF5(X0,X1,X2,X3) = multiply(sF3(X0,X1,X2),sF4(X3)),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
fof(f14,plain,
! [X2,X3,X0,X1] : multiply(sF3(X0,X1,X2),sF4(X3)) = sF5(X0,X1,X2,X3),
inference(reorient_equations,[],[f13]) ).
fof(f15,definition,
! [X2,X3,X0,X1] : sF6(X0,X1,X2,X3) = inverse(sF5(X0,X1,X2,X3)),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f16,plain,
! [X2,X3,X0,X1] : inverse(sF5(X0,X1,X2,X3)) = sF6(X0,X1,X2,X3),
inference(reorient_equations,[],[f15]) ).
fof(f17,plain,
! [X2,X3,X0,X1] : sF6(X0,X1,X2,X3) = X2,
inference(definition_folding,[],[f1,f16,f14,f12,f10,f8,f6,f4]) ).
fof(f18,definition,
sF7 = inverse(a1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
fof(f19,plain,
inverse(a1) = sF7,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF8 = multiply(sF7,a1),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
fof(f21,plain,
multiply(sF7,a1) = sF8,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF9 = inverse(b1),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
fof(f23,plain,
inverse(b1) = sF9,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF10 = multiply(sF9,b1),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
fof(f25,plain,
multiply(sF9,b1) = sF10,
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
sF8 != sF10,
inference(definition_folding,[],[f2,f25,f23,f21,f19]) ).
fof(f27,plain,
! [X2,X3,X0,X1] : inverse(sF5(X0,X1,X2,X3)) = X2,
inference(forward_demodulation,[],[f17,f16]) ).
fof(f28,plain,
! [X2,X3,X0,X1] : inverse(multiply(sF3(X0,X1,X2),sF4(X3))) = X2,
inference(forward_demodulation,[],[f27,f14]) ).
fof(f29,plain,
! [X2,X3,X0,X1] : inverse(multiply(sF3(X0,X1,X2),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f28,f12]) ).
fof(f30,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(sF2(X0,X1,X2),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f29,f10]) ).
fof(f31,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(sF1(X0,X1,X2),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f30,f8]) ).
fof(f32,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(sF0(X0,X1,X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f31,f6]) ).
fof(f33,plain,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
inference(forward_demodulation,[],[f32,f4]) ).
fof(f36,plain,
! [X2,X3,X0,X1,X4] : multiply(X3,inverse(X3)) = inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X4,inverse(X4)))),
inference(superposition,[],[f33,f33]) ).
fof(f38,plain,
! [X2,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(a1,sF7))) = X2,
inference(superposition,[],[f33,f19]) ).
fof(f94,plain,
! [X2,X0,X1] : multiply(a1,sF7) = inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(a1,sF7))),
inference(superposition,[],[f38,f38]) ).
fof(f176,plain,
! [X0,X1] : multiply(X0,inverse(X0)) = multiply(X1,inverse(X1)),
inference(superposition,[],[f36,f36]) ).
fof(f212,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(a1,sF7),
inference(superposition,[],[f176,f19]) ).
fof(f340,plain,
! [X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(a1,sF7),X1)),X0),inverse(X0)),multiply(a1,sF7))) = X1,
inference(superposition,[],[f38,f212]) ).
fof(f345,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = inverse(multiply(multiply(multiply(inverse(multiply(a1,sF7)),X0),X1),multiply(a1,sF7))),
inference(superposition,[],[f38,f212]) ).
fof(f482,plain,
! [X0] : inverse(multiply(multiply(multiply(a1,sF7),inverse(inverse(inverse(multiply(multiply(a1,sF7),X0))))),multiply(a1,sF7))) = X0,
inference(superposition,[],[f340,f212]) ).
fof(f539,plain,
! [X0] : inverse(multiply(inverse(inverse(multiply(a1,sF7))),X0)) = inverse(multiply(multiply(multiply(a1,sF7),X0),multiply(a1,sF7))),
inference(superposition,[],[f345,f212]) ).
fof(f910,plain,
! [X0] : inverse(multiply(inverse(inverse(multiply(a1,sF7))),inverse(inverse(inverse(multiply(multiply(a1,sF7),X0)))))) = X0,
inference(superposition,[],[f539,f482]) ).
fof(f1460,plain,
! [X0,X1] : multiply(a1,sF7) = inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(a1,sF7)))),X0),X1)),
inference(superposition,[],[f94,f345]) ).
fof(f1508,plain,
! [X0] : multiply(a1,sF7) = inverse(multiply(multiply(inverse(multiply(multiply(a1,sF7),inverse(multiply(a1,sF7)))),X0),inverse(X0))),
inference(superposition,[],[f1460,f212]) ).
fof(f1577,plain,
! [X0] : multiply(a1,sF7) = inverse(multiply(multiply(inverse(multiply(a1,sF7)),X0),inverse(X0))),
inference(forward_demodulation,[],[f1508,f212]) ).
fof(f1742,plain,
multiply(a1,sF7) = inverse(multiply(multiply(multiply(a1,sF7),inverse(multiply(a1,sF7))),multiply(a1,sF7))),
inference(superposition,[],[f1460,f1577]) ).
fof(f1746,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(multiply(multiply(a1,sF7),inverse(multiply(a1,sF7))),X0),multiply(a1,sF7))),
inference(superposition,[],[f38,f1577]) ).
fof(f1768,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(multiply(a1,sF7),X0),multiply(a1,sF7))),
inference(forward_demodulation,[],[f1746,f212]) ).
fof(f1772,plain,
multiply(a1,sF7) = inverse(multiply(multiply(a1,sF7),multiply(a1,sF7))),
inference(forward_demodulation,[],[f1742,f212]) ).
fof(f1824,plain,
inverse(inverse(multiply(a1,sF7))) = inverse(multiply(multiply(a1,sF7),multiply(a1,sF7))),
inference(superposition,[],[f1768,f212]) ).
fof(f1863,plain,
multiply(a1,sF7) = inverse(inverse(multiply(a1,sF7))),
inference(forward_demodulation,[],[f1824,f1772]) ).
fof(f1870,plain,
! [X0] : inverse(multiply(multiply(a1,sF7),X0)) = inverse(multiply(multiply(multiply(a1,sF7),X0),multiply(a1,sF7))),
inference(superposition,[],[f539,f1863]) ).
fof(f1883,plain,
! [X0] : inverse(X0) = inverse(multiply(multiply(a1,sF7),X0)),
inference(forward_demodulation,[],[f1870,f1768]) ).
fof(f1889,plain,
multiply(a1,sF7) = inverse(multiply(a1,sF7)),
inference(superposition,[],[f1883,f1772]) ).
fof(f1895,plain,
! [X0] : inverse(multiply(inverse(inverse(multiply(a1,sF7))),inverse(inverse(inverse(X0))))) = X0,
inference(superposition,[],[f910,f1883]) ).
fof(f1930,plain,
! [X0] : inverse(multiply(multiply(a1,sF7),inverse(inverse(inverse(X0))))) = X0,
inference(forward_demodulation,[],[f1895,f1863]) ).
fof(f1938,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(forward_demodulation,[],[f1930,f1883]) ).
fof(f1980,plain,
! [X0] : multiply(multiply(a1,sF7),X0) = inverse(inverse(inverse(inverse(X0)))),
inference(superposition,[],[f1938,f1883]) ).
fof(f1986,plain,
a1 = inverse(inverse(inverse(sF7))),
inference(superposition,[],[f1938,f19]) ).
fof(f1987,plain,
b1 = inverse(inverse(inverse(sF9))),
inference(superposition,[],[f1938,f23]) ).
fof(f2008,plain,
! [X0] : multiply(multiply(a1,sF7),X0) = X0,
inference(forward_demodulation,[],[f1980,f1938]) ).
fof(f2058,plain,
multiply(a1,sF7) = multiply(inverse(inverse(sF7)),a1),
inference(superposition,[],[f212,f1986]) ).
fof(f2077,plain,
multiply(a1,sF7) = multiply(inverse(inverse(sF9)),b1),
inference(superposition,[],[f212,f1987]) ).
fof(f2097,plain,
! [X0] : inverse(X0) = inverse(multiply(X0,multiply(a1,sF7))),
inference(superposition,[],[f1768,f2008]) ).
fof(f2572,plain,
! [X0] : multiply(X0,multiply(a1,sF7)) = inverse(inverse(inverse(inverse(X0)))),
inference(superposition,[],[f1938,f2097]) ).
fof(f2573,plain,
! [X0] : multiply(X0,multiply(a1,sF7)) = X0,
inference(forward_demodulation,[],[f2572,f1938]) ).
fof(f2781,plain,
! [X0] : inverse(multiply(multiply(inverse(multiply(multiply(a1,sF7),X0)),inverse(multiply(a1,sF7))),multiply(a1,sF7))) = X0,
inference(superposition,[],[f340,f2573]) ).
fof(f2810,plain,
! [X0] : inverse(multiply(inverse(multiply(multiply(a1,sF7),X0)),inverse(multiply(a1,sF7)))) = X0,
inference(forward_demodulation,[],[f2781,f2097]) ).
fof(f2899,plain,
! [X0] : inverse(multiply(inverse(multiply(multiply(a1,sF7),X0)),multiply(a1,sF7))) = X0,
inference(forward_demodulation,[],[f2810,f1889]) ).
fof(f2966,plain,
! [X0] : inverse(inverse(multiply(multiply(a1,sF7),X0))) = X0,
inference(forward_demodulation,[],[f2899,f2097]) ).
fof(f2990,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[],[f2966,f1883]) ).
fof(f3064,plain,
multiply(sF7,a1) = multiply(a1,sF7),
inference(superposition,[],[f2058,f2990]) ).
fof(f3066,plain,
multiply(sF9,b1) = multiply(a1,sF7),
inference(superposition,[],[f2077,f2990]) ).
fof(f3085,plain,
sF10 = multiply(a1,sF7),
inference(forward_demodulation,[],[f3066,f25]) ).
fof(f3086,plain,
sF8 = multiply(a1,sF7),
inference(forward_demodulation,[],[f3064,f21]) ).
fof(f3394,plain,
sF8 = sF10,
inference(forward_demodulation,[],[f3086,f3085]) ).
fof(f3397,plain,
sF8 != sF8,
inference(superposition,[],[f26,f3394]) ).
fof(f3410,plain,
$false,
inference(trivial_inequality_removal,[],[f3397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP433-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n001.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 10:10:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 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
% 3.14/1.13 % (3322867)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.14/1.13 % (3322877)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2899203898:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.14/1.13 % (3322875)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3649231467:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.14/1.13 % (3322874)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=443494513:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.14/1.13 % (3322873)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=821733003:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.14/1.13 % (3322872)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=1454500922:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.14/1.13 % (3322878)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=533570925:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.14/1.13 % (3322876)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1593502501:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.14/1.13 % (3322875)Instruction limit reached!
% 3.14/1.13 % (3322875)------------------------------
% 3.14/1.13 % (3322875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.13 % (3322875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.13 % (3322875)CaDiCaL version: 2.1.3
% 3.14/1.13 % (3322875)Termination reason: Instruction limit
% 3.14/1.13 % (3322875)Termination phase: Saturation
% 3.14/1.13 % (3322875)Time elapsed: 0.073 s
% 3.14/1.13 % (3322875)Peak memory usage: 88 MB
% 3.14/1.13 % (3322875)Instructions burned: 137 (million)
% 3.14/1.13 % (3322876)First to succeed.
% 3.14/1.13 % (3322876)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3322867"
% 3.14/1.13 % (3322877)Instruction limit reached!
% 3.14/1.13 % (3322877)------------------------------
% 3.14/1.13 % (3322877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.13 % (3322877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.13 % (3322877)CaDiCaL version: 2.1.3
% 3.14/1.13 % (3322877)Termination reason: Instruction limit
% 3.14/1.13 % (3322877)Termination phase: Saturation
% 3.14/1.13 % (3322877)Time elapsed: 0.085 s
% 3.14/1.13 % (3322877)Peak memory usage: 90 MB
% 3.14/1.13 % (3322877)Instructions burned: 257 (million)
% 3.14/1.13 % (3322887)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1140555432:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.14/1.13 % (3322886)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1027251958:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.14/1.13 % (3322876)Refutation found. Thanks to Tanya!
% 3.14/1.13 % SZS status Unsatisfiable for theBenchmark
% 3.14/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 3.95/1.23 % (3322876)------------------------------
% 3.95/1.23 % (3322876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.95/1.23 % (3322876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.95/1.23 % (3322876)CaDiCaL version: 2.1.3
% 3.95/1.23 % (3322876)Termination reason: Refutation
% 3.95/1.23 % (3322876)Time elapsed: 0.083 s
% 3.95/1.23 % (3322876)Peak memory usage: 89 MB
% 3.95/1.23 % (3322876)Instructions burned: 158 (million)
% 3.95/1.23 % (3322876)------------------------------
% 3.95/1.23 % (3322876)------------------------------
% 3.95/1.23 % (3322867)Success in time 0.518 s
% 3.95/1.23 % Vampire exiting
%------------------------------------------------------------------------------