%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP660-11 : 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 : n016.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 10:15:28 AM UTC 2026
% Result : Unsatisfiable 10.27s 2.34s
% Output : Refutation 10.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 49 unt; 2 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 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,axiom,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X2),X0) = mult(X0,mult(X1,mult(X2,X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,negated_conjecture,
mult(x0,rd(x1,x1)) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
fof(f7,plain,
x0 != mult(x0,rd(x1,x1)),
inference(reorient_equations,[],[f6]) ).
fof(f8,definition,
sF0 = rd(x1,x1),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f9,plain,
rd(x1,x1) = sF0,
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
sF1 = mult(x0,sF0),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f11,plain,
mult(x0,sF0) = sF1,
inference(reorient_equations,[],[f10]) ).
fof(f12,plain,
x0 != sF1,
inference(definition_folding,[],[f7,f11,f9]) ).
fof(f14,plain,
! [X2,X0,X1] : mult(X1,mult(ld(X1,X0),mult(X2,X1))) = mult(mult(X0,X2),X1),
inference(superposition,[],[f5,f1]) ).
fof(f17,plain,
! [X2,X0,X1] : mult(X0,X1) = mult(X1,mult(X2,mult(ld(mult(X1,X2),X0),X1))),
inference(superposition,[],[f5,f1]) ).
fof(f20,plain,
x1 = mult(sF0,x1),
inference(superposition,[],[f3,f9]) ).
fof(f21,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(superposition,[],[f2,f3]) ).
fof(f41,plain,
x1 = ld(sF0,x1),
inference(superposition,[],[f21,f9]) ).
fof(f74,plain,
! [X2,X0,X1] : mult(ld(X2,X0),mult(X1,X2)) = ld(X2,mult(mult(X0,X1),X2)),
inference(superposition,[],[f2,f14]) ).
fof(f79,plain,
! [X2,X0,X1] : mult(ld(X1,X2),mult(ld(X2,X0),X1)) = ld(X1,mult(X0,X1)),
inference(superposition,[],[f74,f1]) ).
fof(f82,plain,
! [X2,X0,X1] : ld(X1,mult(X0,X1)) = mult(ld(X1,rd(X0,X2)),mult(X2,X1)),
inference(superposition,[],[f74,f3]) ).
fof(f90,plain,
! [X0,X1] : mult(X0,X1) = mult(ld(mult(X0,X1),X0),mult(X1,mult(X0,X1))),
inference(superposition,[],[f2,f74]) ).
fof(f114,plain,
! [X2,X0,X1] : mult(X2,mult(ld(mult(X1,X2),X0),X1)) = ld(X1,mult(X0,X1)),
inference(superposition,[],[f2,f17]) ).
fof(f153,plain,
! [X2,X0,X1] : mult(ld(mult(X0,X2),X1),X0) = ld(X2,ld(X0,mult(X1,X0))),
inference(superposition,[],[f2,f114]) ).
fof(f176,plain,
! [X0,X1] : ld(X1,X0) = mult(ld(mult(X0,X1),X0),X0),
inference(superposition,[],[f153,f2]) ).
fof(f199,plain,
! [X0,X1] : ld(mult(X1,X0),X1) = rd(ld(X0,X1),X1),
inference(superposition,[],[f4,f176]) ).
fof(f207,plain,
! [X0,X1] : mult(X0,X1) = mult(rd(ld(X1,X0),X0),mult(X1,mult(X0,X1))),
inference(backward_demodulation,[],[f90,f199]) ).
fof(f230,plain,
! [X0,X1] : mult(mult(X1,X0),rd(ld(X0,X1),X1)) = X1,
inference(superposition,[],[f1,f199]) ).
fof(f255,plain,
x1 = mult(mult(x1,sF0),rd(x1,x1)),
inference(superposition,[],[f230,f41]) ).
fof(f269,plain,
x1 = mult(mult(x1,sF0),sF0),
inference(forward_demodulation,[],[f255,f9]) ).
fof(f855,plain,
! [X2,X0,X1] : ld(X0,rd(X1,X2)) = rd(ld(X0,mult(X1,X0)),mult(X2,X0)),
inference(superposition,[],[f4,f82]) ).
fof(f1665,plain,
x1 = mult(rd(ld(sF0,mult(x1,sF0)),mult(x1,sF0)),mult(sF0,x1)),
inference(superposition,[],[f207,f269]) ).
fof(f1710,plain,
x1 = mult(rd(ld(sF0,mult(x1,sF0)),mult(x1,sF0)),x1),
inference(forward_demodulation,[],[f1665,f20]) ).
fof(f1738,plain,
x1 = mult(ld(sF0,rd(x1,x1)),x1),
inference(forward_demodulation,[],[f1710,f855]) ).
fof(f1748,plain,
x1 = mult(ld(sF0,sF0),x1),
inference(forward_demodulation,[],[f1738,f9]) ).
fof(f1761,plain,
rd(x1,x1) = ld(sF0,sF0),
inference(superposition,[],[f4,f1748]) ).
fof(f1790,plain,
sF0 = ld(sF0,sF0),
inference(forward_demodulation,[],[f1761,f9]) ).
fof(f1813,plain,
sF0 = mult(sF0,sF0),
inference(superposition,[],[f1,f1790]) ).
fof(f1817,plain,
! [X0] : ld(sF0,mult(X0,sF0)) = mult(sF0,mult(ld(sF0,X0),sF0)),
inference(superposition,[],[f79,f1790]) ).
fof(f2214,plain,
! [X0] : mult(sF0,mult(ld(sF0,X0),sF0)) = mult(mult(X0,sF0),sF0),
inference(superposition,[],[f14,f1813]) ).
fof(f2226,plain,
! [X0] : ld(sF0,rd(X0,sF0)) = rd(ld(sF0,mult(X0,sF0)),sF0),
inference(superposition,[],[f855,f1813]) ).
fof(f2239,plain,
! [X0] : ld(sF0,mult(X0,sF0)) = mult(mult(X0,sF0),sF0),
inference(backward_demodulation,[],[f1817,f2214]) ).
fof(f2254,plain,
! [X0] : ld(sF0,rd(X0,sF0)) = rd(mult(mult(X0,sF0),sF0),sF0),
inference(backward_demodulation,[],[f2226,f2239]) ).
fof(f2256,plain,
! [X0] : mult(X0,sF0) = ld(sF0,rd(X0,sF0)),
inference(forward_demodulation,[],[f2254,f4]) ).
fof(f2279,plain,
! [X0] : ld(sF0,X0) = mult(mult(X0,sF0),sF0),
inference(superposition,[],[f2256,f4]) ).
fof(f2319,plain,
! [X0] : ld(sF0,X0) = ld(sF0,mult(X0,sF0)),
inference(backward_demodulation,[],[f2239,f2279]) ).
fof(f2356,plain,
! [X0] : mult(X0,sF0) = mult(sF0,ld(sF0,X0)),
inference(superposition,[],[f1,f2319]) ).
fof(f2371,plain,
! [X0] : mult(X0,sF0) = X0,
inference(forward_demodulation,[],[f2356,f1]) ).
fof(f2448,plain,
x0 = sF1,
inference(backward_demodulation,[],[f11,f2371]) ).
fof(f2494,plain,
$false,
inference(forward_subsumption_resolution,[],[f2448,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660-11 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n016.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 10:37:47 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 9.85/2.24 % (2428139)Detected a unit-equality problem, will run specialized UEQ schedule.
% 9.85/2.24 % (2428148)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3195098944:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 9.85/2.24 % (2428147)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1779142551:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 9.85/2.24 % (2428146)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1323695832:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 9.85/2.24 % (2428145)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=2891334349:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 9.85/2.24 % (2428144)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=2404514959:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 9.85/2.24 % (2428150)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3816472494:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 9.85/2.24 % (2428149)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2873821100:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 9.85/2.24 % (2428148)Instruction limit reached!
% 9.85/2.24 % (2428148)------------------------------
% 9.85/2.24 % (2428148)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.85/2.24 % (2428148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.85/2.24 % (2428148)CaDiCaL version: 2.1.3
% 9.85/2.24 % (2428148)Termination reason: Instruction limit
% 9.85/2.24 % (2428148)Termination phase: Saturation
% 9.85/2.24 % (2428148)Time elapsed: 0.058 s
% 9.85/2.24 % (2428148)Peak memory usage: 89 MB
% 9.85/2.24 % (2428148)Instructions burned: 181 (million)
% 9.85/2.24 % (2428147)Instruction limit reached!
% 9.85/2.24 % (2428147)------------------------------
% 9.85/2.24 % (2428147)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.85/2.24 % (2428147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.85/2.24 % (2428147)CaDiCaL version: 2.1.3
% 9.85/2.24 % (2428147)Termination reason: Instruction limit
% 9.85/2.24 % (2428147)Termination phase: Saturation
% 9.85/2.24 % (2428147)Time elapsed: 0.085 s
% 9.85/2.24 % (2428147)Peak memory usage: 88 MB
% 9.85/2.24 % (2428147)Instructions burned: 138 (million)
% 9.85/2.24 % (2428158)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=968274373:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 9.85/2.24 % (2428149)Instruction limit reached!
% 9.85/2.24 % (2428149)------------------------------
% 9.85/2.24 % (2428149)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.85/2.24 % (2428149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.85/2.24 % (2428149)CaDiCaL version: 2.1.3
% 9.85/2.24 % (2428149)Termination reason: Instruction limit
% 9.85/2.24 % (2428149)Termination phase: Saturation
% 9.85/2.24 % (2428149)Time elapsed: 0.145 s
% 9.85/2.24 % (2428149)Peak memory usage: 91 MB
% 9.85/2.24 % (2428149)Instructions burned: 258 (million)
% 9.85/2.24 % (2428159)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1260299731:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 9.85/2.24 % (2428161)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3654889390:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 9.85/2.24 % (2428161)Instruction limit reached!
% 9.85/2.24 % (2428161)------------------------------
% 9.85/2.24 % (2428161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.85/2.24 % (2428161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.85/2.24 % (2428161)CaDiCaL version: 2.1.3
% 9.85/2.24 % (2428161)Termination reason: Instruction limit
% 9.85/2.24 % (2428161)Termination phase: Saturation
% 9.85/2.24 % (2428161)Time elapsed: 0.115 s
% 10.27/2.34 % (2428161)Peak memory usage: 90 MB
% 10.27/2.34 % (2428161)Instructions burned: 216 (million)
% 10.27/2.34 % (2428164)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=1820135247:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2994 on theBenchmark for (2994ds/317Mi)
% 10.27/2.34 % (2428150)Instruction limit reached!
% 10.27/2.34 % (2428150)------------------------------
% 10.27/2.34 % (2428150)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.27/2.34 % (2428150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.27/2.34 % (2428150)CaDiCaL version: 2.1.3
% 10.27/2.34 % (2428150)Termination reason: Instruction limit
% 10.27/2.34 % (2428150)Termination phase: Saturation
% 10.27/2.34 % (2428150)Time elapsed: 0.679 s
% 10.27/2.34 % (2428150)Peak memory usage: 101 MB
% 10.27/2.34 % (2428150)Instructions burned: 1188 (million)
% 10.27/2.34 % (2428164)Instruction limit reached!
% 10.27/2.34 % (2428164)------------------------------
% 10.27/2.34 % (2428164)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.27/2.34 % (2428164)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.27/2.34 % (2428164)CaDiCaL version: 2.1.3
% 10.27/2.34 % (2428164)Termination reason: Instruction limit
% 10.27/2.34 % (2428164)Termination phase: Saturation
% 10.27/2.34 % (2428164)Time elapsed: 0.197 s
% 10.27/2.34 % (2428164)Peak memory usage: 93 MB
% 10.27/2.34 % (2428164)Instructions burned: 318 (million)
% 10.27/2.34 % (2428158)Instruction limit reached!
% 10.27/2.34 % (2428158)------------------------------
% 10.27/2.34 % (2428158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.27/2.34 % (2428158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.27/2.34 % (2428158)CaDiCaL version: 2.1.3
% 10.27/2.34 % (2428158)Termination reason: Instruction limit
% 10.27/2.34 % (2428158)Termination phase: Saturation
% 10.27/2.34 % (2428158)Time elapsed: 0.703 s
% 10.27/2.34 % (2428158)Peak memory usage: 141 MB
% 10.27/2.34 % (2428158)Instructions burned: 2054 (million)
% 10.27/2.34 % (2428166)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=692721654:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 10.27/2.34 % (2428167)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2319726649:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 10.27/2.34 % (2428146)First to succeed.
% 10.27/2.34 % (2428146)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2428139"
% 10.27/2.34 % (2428168)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:lma=off:kmz=on:random_seed=3656843296:i=14534:kws=arity:fgj=on:bd=preordered:ins=6:ss=axioms:sgt=30_2989 on theBenchmark for (2989ds/14534Mi)
% 10.27/2.34 % (2428146)Refutation found. Thanks to Tanya!
% 10.27/2.34 % SZS status Unsatisfiable for theBenchmark
% 10.27/2.34 % SZS output start Proof for theBenchmark
% See solution above
% 10.27/2.35 % (2428146)------------------------------
% 10.27/2.35 % (2428146)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.27/2.35 % (2428146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.27/2.35 % (2428146)CaDiCaL version: 2.1.3
% 10.27/2.35 % (2428146)Termination reason: Refutation
% 10.27/2.35 % (2428146)Time elapsed: 0.969 s
% 10.27/2.35 % (2428146)Peak memory usage: 134 MB
% 10.27/2.35 % (2428146)Instructions burned: 1507 (million)
% 10.27/2.35 % (2428146)------------------------------
% 10.27/2.35 % (2428146)------------------------------
% 10.27/2.35 % (2428139)Success in time 1.385 s
% 10.27/2.35 % Vampire exiting
%------------------------------------------------------------------------------