%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 10:18:33 AM UTC 2026
% Result : Unsatisfiable 0.57s 0.62s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 57 unt; 0 def)
% Number of atoms : 57 ( 56 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 : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ld(X0,mult(X0,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
fof(f2,axiom,
! [X0] : rd(mult(X0,X0),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
fof(f3,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = ld(X0,mult(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f23,plain,
! [X0,X1] : ld(X0,mult(X0,ld(X1,X1))) = mult(rd(rd(X0,X0),X1),X1),
inference(forward_demodulation,[],[f7,f4]) ).
fof(f24,plain,
! [X0,X1] : mult(rd(rd(X0,X0),X1),X1) = mult(X0,ld(X0,ld(X1,X1))),
inference(forward_demodulation,[],[f23,f3]) ).
fof(f25,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(X0,X0))),
inference(superposition,[],[f24,f17]) ).
fof(f26,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,ld(rd(X0,X0),rd(X0,X0)))),
inference(superposition,[],[f24,f13]) ).
fof(f31,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(superposition,[],[f25,f11]) ).
fof(f48,plain,
! [X0] : rd(X0,X0) = mult(X0,ld(X0,rd(rd(X0,X0),rd(X0,X0)))),
inference(forward_demodulation,[],[f26,f31]) ).
fof(f65,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(f66,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,[],[f65,f3]) ).
fof(f67,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(f68,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,[],[f67,f4]) ).
fof(f69,plain,
! [X2,X0,X1] : mult(mult(X0,ld(X0,X1)),X2) = mult(X0,ld(X0,mult(X1,X2))),
inference(superposition,[],[f66,f1]) ).
fof(f99,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,ld(X0,mult(X0,X1))),
inference(superposition,[],[f69,f9]) ).
fof(f101,plain,
! [X0,X1] : mult(ld(X0,X0),X1) = mult(X0,ld(X0,mult(ld(X0,X0),X1))),
inference(superposition,[],[f69,f11]) ).
fof(f137,plain,
! [X0,X1] : mult(rd(X0,X0),X1) = mult(X0,ld(X0,mult(rd(X0,X0),X1))),
inference(forward_demodulation,[],[f101,f31]) ).
fof(f139,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(X0,ld(X0,X1))),
inference(forward_demodulation,[],[f99,f3]) ).
fof(f240,plain,
! [X0] : rd(rd(X0,X0),rd(X0,X0)) = mult(X0,ld(X0,rd(rd(X0,X0),rd(X0,X0)))),
inference(superposition,[],[f137,f48]) ).
fof(f256,plain,
! [X0] : rd(X0,X0) = rd(rd(X0,X0),rd(X0,X0)),
inference(forward_demodulation,[],[f240,f48]) ).
fof(f716,plain,
! [X2,X0,X1] : mult(X0,mult(rd(ld(X0,X0),X1),X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(superposition,[],[f68,f9]) ).
fof(f750,plain,
! [X2,X0,X1] : mult(X1,mult(rd(X2,X0),X0)) = mult(rd(mult(X1,X2),X0),X0),
inference(superposition,[],[f68,f2]) ).
fof(f786,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,[],[f716,f31]) ).
fof(f800,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,[],[f786,f24]) ).
fof(f808,plain,
! [X2,X0,X1] : mult(X0,ld(X1,X1)) = mult(rd(X0,rd(X2,X1)),rd(X2,X1)),
inference(forward_demodulation,[],[f800,f139]) ).
fof(f811,plain,
! [X2,X0,X1] : mult(rd(X0,rd(X2,X1)),rd(X2,X1)) = mult(X0,rd(X1,X1)),
inference(forward_demodulation,[],[f808,f31]) ).
fof(f813,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(rd(ld(X0,X0),X1),X1)),
inference(superposition,[],[f750,f9]) ).
fof(f847,plain,
! [X0,X1] : mult(X0,mult(rd(X1,X1),X1)) = mult(mult(rd(X0,X1),X1),X1),
inference(superposition,[],[f750,f4]) ).
fof(f863,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(rd(X0,X1),X1),X1),
inference(forward_demodulation,[],[f847,f13]) ).
fof(f889,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(rd(rd(X0,X0),X1),X1)),
inference(forward_demodulation,[],[f813,f31]) ).
fof(f909,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,mult(X0,ld(X0,ld(X1,X1)))),
inference(forward_demodulation,[],[f889,f24]) ).
fof(f917,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[],[f909,f139]) ).
fof(f919,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = mult(X0,rd(X1,X1)),
inference(forward_demodulation,[],[f917,f31]) ).
fof(f945,plain,
! [X0,X1] : mult(mult(rd(X0,X1),X1),X1) = mult(mult(X0,X1),rd(X1,X1)),
inference(superposition,[],[f919,f4]) ).
fof(f960,plain,
mult(rd(a,c),c) != mult(a,rd(mult(b,c),mult(b,c))),
inference(superposition,[],[f16,f919]) ).
fof(f976,plain,
mult(a,rd(mult(b,c),mult(b,c))) != mult(a,rd(c,c)),
inference(forward_demodulation,[],[f960,f919]) ).
fof(f984,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f945,f863]) ).
fof(f1343,plain,
! [X0,X1] : rd(mult(X0,X1),rd(X1,X1)) = mult(rd(mult(X0,X1),rd(X1,X1)),rd(X1,X1)),
inference(superposition,[],[f4,f984]) ).
fof(f1351,plain,
! [X0,X1] : mult(mult(X0,X1),rd(rd(X1,X1),rd(X1,X1))) = rd(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f1343,f919]) ).
fof(f1376,plain,
! [X0,X1] : mult(mult(X0,X1),rd(X1,X1)) = rd(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f1351,f256]) ).
fof(f1385,plain,
! [X0,X1] : mult(X0,X1) = rd(mult(X0,X1),rd(X1,X1)),
inference(forward_demodulation,[],[f1376,f984]) ).
fof(f1771,plain,
! [X2,X0,X1] : mult(X0,rd(X1,X1)) = mult(X0,rd(rd(X2,X1),rd(X2,X1))),
inference(forward_demodulation,[],[f811,f919]) ).
fof(f1780,plain,
! [X2,X0,X1] : mult(X2,rd(rd(X1,X1),rd(X1,X1))) = mult(X2,rd(mult(X0,X1),mult(X0,X1))),
inference(superposition,[],[f1771,f1385]) ).
fof(f1882,plain,
! [X2,X0,X1] : mult(X2,rd(X1,X1)) = mult(X2,rd(mult(X0,X1),mult(X0,X1))),
inference(forward_demodulation,[],[f1780,f1771]) ).
fof(f3634,plain,
mult(a,rd(c,c)) != mult(a,rd(c,c)),
inference(superposition,[],[f976,f1882]) ).
fof(f3635,plain,
$false,
inference(trivial_inequality_removal,[],[f3634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.18/0.45 % Computer : n009.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Sun Sep 27 10:36:00 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.24/0.51 Running first-order model finding
% 0.24/0.51 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.62 % (1838941)Will run a generic schedule for satisfiability detection.
% 0.57/0.62 % (1838948)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2989223914:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.57/0.62 % (1838951)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2024345791:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.57/0.62 % (1838947)% WARNING: option uhcvi not known.
% 0.57/0.62 % (1838949)dis+10_1_sil=32000:sp=arity:random_seed=2862302383:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.57/0.62 % (1838946)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3347219761_2999 on theBenchmark for (2999ds/0Mi)
% 0.57/0.62 % (1838950)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2855129318:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.57/0.62 % (1838947)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3474445574:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.57/0.62 % TRYING [1]
% 0.57/0.62 % (1838952)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2532404385:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.57/0.62 % TRYING [2]
% 0.57/0.62 % TRYING [3]
% 0.57/0.62 % TRYING [4]
% 0.57/0.62 % (1838948) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1838941-1838948"...
% 0.57/0.62 % (1838948)...printing done.
% 0.57/0.62 % (1838948)Refutation found. Thanks to Tanya!
% 0.57/0.62 % SZS status Unsatisfiable for theBenchmark
% 0.57/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 0.57/0.62 % (1838948)------------------------------
% 0.57/0.62 % (1838948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.57/0.62 % (1838948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.57/0.62 % (1838948)CaDiCaL version: 2.1.3
% 0.57/0.62 % (1838948)Termination reason: Refutation
% 0.57/0.62 % (1838948)Time elapsed: 0.070 s
% 0.57/0.62 % (1838948)Peak memory usage: 12 MB
% 0.57/0.62 % (1838948)Instructions burned: 141 (million)
% 0.57/0.62 % (1838941)Success in time 0.095 s
% 0.57/0.62 % Vampire exiting
%------------------------------------------------------------------------------