%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP684-1 : 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 : n010.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 10:15:36 AM UTC 2026
% Result : Unsatisfiable 3.05s 1.49s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 65 ( 65 unt; 0 def)
% Number of atoms : 65 ( 64 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
fof(f5,axiom,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(ld(X0,mult(X0,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
fof(f7,axiom,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = rd(mult(rd(X0,X0),X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
fof(f8,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f9,plain,
! [X0] : mult(X0,ld(X0,X0)) = X0,
inference(superposition,[],[f3,f1]) ).
fof(f11,plain,
! [X0] : ld(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f3,f9]) ).
fof(f13,plain,
! [X0] : mult(rd(X0,X0),X0) = X0,
inference(superposition,[],[f4,f2]) ).
fof(f14,plain,
rd(mult(a,c),c) != mult(rd(a,mult(b,c)),mult(b,c)),
inference(superposition,[],[f8,f4]) ).
fof(f16,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
inference(forward_demodulation,[],[f14,f4]) ).
fof(f17,plain,
! [X0] : rd(X0,X0) = mult(rd(rd(X0,X0),X0),X0),
inference(superposition,[],[f4,f13]) ).
fof(f19,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(forward_demodulation,[],[f7,f4]) ).
fof(f20,plain,
! [X0,X1] : mult(rd(rd(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(forward_demodulation,[],[f19,f3]) ).
fof(f25,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f20,f17]) ).
fof(f31,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(superposition,[],[f25,f11]) ).
fof(f35,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,rd(X0,X0))),
inference(superposition,[],[f25,f31]) ).
fof(f38,plain,
! [X2,X3,X0,X1] : ld(ld(X0,X1),mult(ld(X0,X1),mult(X2,X3))) = mult(mult(X0,ld(X0,X2)),X3),
inference(forward_demodulation,[],[f5,f3]) ).
fof(f39,plain,
! [X2,X3,X0,X1] : mult(mult(X0,ld(X0,X2)),X3) = mult(ld(X0,X1),ld(ld(X0,X1),mult(X2,X3))),
inference(forward_demodulation,[],[f38,f3]) ).
fof(f50,plain,
! [X2,X3,X0,X1] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,mult(rd(X1,X3),X3)),
inference(forward_demodulation,[],[f6,f4]) ).
fof(f51,plain,
! [X2,X3,X0,X1] : mult(X0,mult(rd(X1,X3),X3)) = mult(rd(mult(X0,X1),rd(X2,X3)),rd(X2,X3)),
inference(forward_demodulation,[],[f50,f4]) ).
fof(f66,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(superposition,[],[f39,f1]) ).
fof(f95,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,mult(X0,X1))),
inference(superposition,[],[f66,f9]) ).
fof(f132,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f95,f3]) ).
fof(f191,plain,
! [X2,X0,X1] : mult(X0,mult(rd(ld(X0,X0),X1),X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(superposition,[],[f51,f9]) ).
fof(f211,plain,
! [X2,X0,X1] : mult(X1,mult(rd(X2,X0),X0)) = mult(rd(mult(X1,X2),X0),X0),
inference(superposition,[],[f51,f2]) ).
fof(f234,plain,
! [X2,X0,X1] : mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,mult(rd(rd(X0,X0),X1),X1)),
inference(forward_demodulation,[],[f191,f31]) ).
fof(f247,plain,
! [X2,X0,X1] : mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f234,f20]) ).
fof(f252,plain,
! [X2,X0,X1] : mult(X0,ld(X1,X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(forward_demodulation,[],[f247,f132]) ).
fof(f253,plain,
! [X2,X0,X1] : mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,rd(X1,X1)),
inference(forward_demodulation,[],[f252,f31]) ).
fof(f254,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(rd(ld(X0,X0),X1),X1)),
inference(superposition,[],[f211,f9]) ).
fof(f274,plain,
! [X0,X1] : mult(X0,mult(rd(X1,X1),X1)) = mult(mult(rd(X0,X1),X1),X1),
inference(superposition,[],[f211,f4]) ).
fof(f287,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(rd(X0,X1),X1),X1),
inference(forward_demodulation,[],[f274,f13]) ).
fof(f304,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(rd(rd(X0,X0),X1),X1)),
inference(forward_demodulation,[],[f254,f31]) ).
fof(f321,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f304,f20]) ).
fof(f326,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[],[f321,f132]) ).
fof(f327,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(forward_demodulation,[],[f326,f31]) ).
fof(f329,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(mult(X0,ld(X0,ld(X1,X1))),X1),
inference(superposition,[],[f287,f20]) ).
fof(f343,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(X0,ld(X0,mult(ld(X1,X1),X1))),
inference(forward_demodulation,[],[f329,f66]) ).
fof(f346,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(X0,ld(X0,mult(rd(X1,X1),X1))),
inference(forward_demodulation,[],[f343,f31]) ).
fof(f347,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = mult(rd(X0,X0),X1),
inference(forward_demodulation,[],[f346,f13]) ).
fof(f349,plain,
! [X0,X1] : mult(mult(rd(X0,X1),X1),X1) = mult(mult(X0,X1),rd(X1,X1)),
inference(superposition,[],[f327,f4]) ).
fof(f361,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X0,rd(X1,X1)),X1),
inference(superposition,[],[f287,f327]) ).
fof(f363,plain,
mult(rd(a,c),c) != mult(a,rd(mult(b,c),mult(b,c))),
inference(superposition,[],[f16,f327]) ).
fof(f377,plain,
mult(a,rd(mult(b,c),mult(b,c))) != mult(a,rd(c,c)),
inference(forward_demodulation,[],[f363,f327]) ).
fof(f384,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f349,f287]) ).
fof(f430,plain,
! [X0] : rd(X0,X0) = rd(mult(X0,ld(X0,rd(X0,X0))),rd(X0,X0)),
inference(superposition,[],[f2,f347]) ).
fof(f459,plain,
! [X0] : rd(X0,X0) = rd(rd(X0,X0),rd(X0,X0)),
inference(forward_demodulation,[],[f430,f35]) ).
fof(f517,plain,
! [X0,X1] : mult(mult(X0,rd(X1,X1)),X1) = mult(mult(rd(X0,rd(X1,X1)),rd(X1,X1)),X1),
inference(superposition,[],[f361,f287]) ).
fof(f543,plain,
! [X0,X1] : mult(mult(X0,rd(X1,X1)),X1) = mult(rd(X0,rd(X1,X1)),X1),
inference(forward_demodulation,[],[f517,f361]) ).
fof(f553,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(X0,rd(X1,X1)),X1),
inference(forward_demodulation,[],[f543,f361]) ).
fof(f678,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(rd(rd(X0,rd(X1,X1)),X1),X1),
inference(superposition,[],[f4,f553]) ).
fof(f682,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(rd(X0,rd(X1,X1)),rd(X1,X1)),
inference(forward_demodulation,[],[f678,f327]) ).
fof(f691,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(rd(X1,X1),rd(X1,X1))),
inference(forward_demodulation,[],[f682,f327]) ).
fof(f696,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(forward_demodulation,[],[f691,f459]) ).
fof(f709,plain,
! [X0,X1] : mult(mult(X0,X1),rd(rd(X1,X1),rd(X1,X1))) = rd(mult(X0,X1),rd(X1,X1)),
inference(superposition,[],[f696,f384]) ).
fof(f749,plain,
! [X0,X1] : mult(mult(X0,X1),rd(X1,X1)) = rd(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f709,f459]) ).
fof(f767,plain,
! [X0,X1] : mult(X0,X1) = rd(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f749,f384]) ).
fof(f900,plain,
! [X2,X0,X1] : mult(X0,rd(X1,X1)) = mult(X0,rd(rd(X2,X1),rd(X2,X1))),
inference(forward_demodulation,[],[f253,f327]) ).
fof(f908,plain,
! [X2,X0,X1] : mult(X2,rd(rd(X1,X1),rd(X1,X1))) = mult(X2,rd(mult(X0,X1),mult(X0,X1))),
inference(superposition,[],[f900,f767]) ).
fof(f999,plain,
! [X2,X0,X1] : mult(X2,rd(X1,X1)) = mult(X2,rd(mult(X0,X1),mult(X0,X1))),
inference(forward_demodulation,[],[f908,f900]) ).
fof(f5198,plain,
mult(a,rd(c,c)) != mult(a,rd(c,c)),
inference(superposition,[],[f377,f999]) ).
fof(f5199,plain,
$false,
inference(trivial_inequality_removal,[],[f5198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n010.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 10:36:17 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.05/1.49 % (768953)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.05/1.49 % (768970)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=385216478:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 3.05/1.49 % (768972)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=24665068:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 3.05/1.49 % (768969)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=2870386852:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 3.05/1.49 % (768976)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=82949399:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 3.05/1.49 % (768973)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3197772169:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 3.05/1.49 % (768978)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=4287975392:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 3.05/1.49 % (768974)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2622832318:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 3.05/1.49 % (768973)Instruction limit reached!
% 3.05/1.49 % (768973)------------------------------
% 3.05/1.49 % (768973)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.49 % (768973)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.49 % (768973)CaDiCaL version: 2.1.3
% 3.05/1.49 % (768973)Termination reason: Instruction limit
% 3.05/1.49 % (768973)Termination phase: Saturation
% 3.05/1.49 % (768973)Time elapsed: 0.083 s
% 3.05/1.49 % (768973)Peak memory usage: 88 MB
% 3.05/1.49 % (768973)Instructions burned: 136 (million)
% 3.05/1.49 % (768978)First to succeed.
% 3.05/1.49 % (768978)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-768953"
% 3.05/1.49 % (768974)Instruction limit reached!
% 3.05/1.49 % (768974)------------------------------
% 3.05/1.49 % (768974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.49 % (768974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.49 % (768974)CaDiCaL version: 2.1.3
% 3.05/1.49 % (768974)Termination reason: Instruction limit
% 3.05/1.49 % (768974)Termination phase: Saturation
% 3.05/1.49 % (768974)Time elapsed: 0.105 s
% 3.05/1.49 % (768974)Peak memory usage: 89 MB
% 3.05/1.49 % (768974)Instructions burned: 183 (million)
% 3.05/1.49 % (768976)Instruction limit reached!
% 3.05/1.49 % (768976)------------------------------
% 3.05/1.49 % (768976)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.05/1.49 % (768976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.05/1.49 % (768976)CaDiCaL version: 2.1.3
% 3.05/1.49 % (768976)Termination reason: Instruction limit
% 3.05/1.49 % (768976)Termination phase: Saturation
% 3.05/1.49 % (768976)Time elapsed: 0.163 s
% 3.05/1.49 % (768976)Peak memory usage: 89 MB
% 3.05/1.49 % (768976)Instructions burned: 257 (million)
% 3.05/1.49 % (769065)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3880015510:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.05/1.49 % (769069)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1026548496:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.05/1.49 % (769081)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1001982919:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 3.05/1.49 % (768978)Refutation found. Thanks to Tanya!
% 3.05/1.49 % SZS status Unsatisfiable for theBenchmark
% 3.05/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 4.27/1.68 % (768978)------------------------------
% 4.27/1.68 % (768978)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.27/1.68 % (768978)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.27/1.68 % (768978)CaDiCaL version: 2.1.3
% 4.27/1.68 % (768978)Termination reason: Refutation
% 4.27/1.68 % (768978)Time elapsed: 0.098 s
% 4.27/1.68 % (768978)Peak memory usage: 89 MB
% 4.27/1.68 % (768978)Instructions burned: 176 (million)
% 4.27/1.68 % (768978)------------------------------
% 4.27/1.68 % (768978)------------------------------
% 4.27/1.68 % (768953)Success in time 0.504 s
% 4.27/1.68 % Vampire exiting
%------------------------------------------------------------------------------