%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP754-1 : TPTP v9.3.1. Released v4.0.0.
% 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 10:16:07 AM UTC 2026
% Result : Unsatisfiable 10.72s 2.21s
% Output : Refutation 10.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 36 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 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 : 105 ( 105 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(f5,axiom,
! [X2,X0,X1] : mult(X0,mult(X1,X2)) = mult(mult(rd(X0,X0),X1),mult(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f6,axiom,
! [X2,X0,X1] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(X1,ld(X2,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f7,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f16,plain,
! [X2,X0,X1] : mult(X2,ld(X0,X0)) = ld(mult(X1,X0),mult(mult(X1,X2),X0)),
inference(superposition,[],[f2,f6]) ).
fof(f17,plain,
! [X2,X0,X1] : mult(X1,X0) = ld(mult(rd(X1,X1),X2),mult(X1,mult(X2,X0))),
inference(superposition,[],[f2,f5]) ).
fof(f18,plain,
! [X2,X0,X1] : mult(X0,mult(X2,ld(X0,X1))) = mult(mult(rd(X0,X0),X2),X1),
inference(superposition,[],[f5,f1]) ).
fof(f30,plain,
! [X2,X0,X1] : mult(ld(X0,X1),ld(X2,X2)) = ld(mult(X0,X2),mult(X1,X2)),
inference(superposition,[],[f16,f1]) ).
fof(f61,plain,
! [X2,X0,X1] : mult(rd(X1,X1),X0) = rd(mult(X1,mult(X0,ld(X1,X2))),X2),
inference(superposition,[],[f4,f18]) ).
fof(f127,plain,
! [X2,X0,X1] : mult(ld(rd(X0,X1),X2),ld(X1,X1)) = ld(X0,mult(X2,X1)),
inference(superposition,[],[f30,f3]) ).
fof(f133,plain,
! [X2,X0,X1] : mult(ld(X2,rd(X0,X1)),ld(X1,X1)) = ld(mult(X2,X1),X0),
inference(superposition,[],[f30,f3]) ).
fof(f183,plain,
! [X2,X0,X1] : mult(X2,ld(X0,X1)) = ld(mult(rd(X2,X2),X0),mult(X2,X1)),
inference(superposition,[],[f17,f1]) ).
fof(f253,plain,
! [X2,X0,X1] : mult(X0,ld(X2,ld(X0,X1))) = ld(mult(rd(X0,X0),X2),X1),
inference(superposition,[],[f183,f1]) ).
fof(f374,plain,
! [X2,X0,X1] : mult(rd(X1,X1),rd(X0,ld(X1,X2))) = rd(mult(X1,X0),X2),
inference(superposition,[],[f61,f3]) ).
fof(f394,plain,
! [X2,X0,X1] : mult(rd(X0,X0),rd(X2,X1)) = rd(mult(X0,X2),mult(X0,X1)),
inference(superposition,[],[f374,f2]) ).
fof(f406,plain,
! [X2,X0,X1] : rd(X1,ld(X2,X0)) = ld(rd(X2,X2),rd(mult(X2,X1),X0)),
inference(superposition,[],[f2,f374]) ).
fof(f707,plain,
! [X2,X3,X0,X1] : ld(mult(X1,X0),mult(X3,mult(X1,X2))) = mult(ld(mult(rd(X1,X1),rd(X0,X2)),X3),ld(mult(X1,X2),mult(X1,X2))),
inference(superposition,[],[f127,f394]) ).
fof(f744,plain,
! [X2,X3,X0,X1] : ld(mult(X1,X0),mult(X3,mult(X1,X2))) = mult(ld(mult(rd(X1,X1),rd(X0,X2)),X3),mult(ld(X1,X1),ld(X2,X2))),
inference(forward_demodulation,[],[f707,f30]) ).
fof(f746,plain,
! [X2,X3,X0,X1] : ld(mult(X1,X0),mult(X3,mult(X1,X2))) = mult(mult(X1,ld(rd(X0,X2),ld(X1,X3))),mult(ld(X1,X1),ld(X2,X2))),
inference(forward_demodulation,[],[f744,f253]) ).
fof(f1097,plain,
! [X2,X0,X1] : ld(mult(rd(X0,X0),X1),mult(X0,X2)) = mult(rd(X2,ld(X0,X1)),ld(X1,X1)),
inference(superposition,[],[f133,f406]) ).
fof(f1107,plain,
! [X2,X0,X1] : mult(rd(X2,ld(X0,X1)),ld(X1,X1)) = mult(X0,ld(X1,ld(X0,mult(X0,X2)))),
inference(forward_demodulation,[],[f1097,f253]) ).
fof(f1116,plain,
! [X2,X0,X1] : mult(X0,ld(X1,X2)) = mult(rd(X2,ld(X0,X1)),ld(X1,X1)),
inference(forward_demodulation,[],[f1107,f2]) ).
fof(f1124,plain,
! [X2,X0,X1] : mult(X0,ld(X2,X2)) = mult(X1,ld(X2,mult(X0,ld(X1,X2)))),
inference(superposition,[],[f1116,f4]) ).
fof(f1164,plain,
! [X2,X0,X1] : mult(X2,ld(mult(X0,X1),mult(X0,X1))) = mult(X0,ld(mult(X0,X1),mult(X2,X1))),
inference(superposition,[],[f1124,f2]) ).
fof(f1230,plain,
! [X2,X0,X1] : mult(X2,ld(mult(X0,X1),mult(X0,X1))) = mult(X0,mult(ld(X0,X2),ld(X1,X1))),
inference(forward_demodulation,[],[f1164,f30]) ).
fof(f1237,plain,
! [X2,X0,X1] : mult(X0,mult(ld(X0,X2),ld(X1,X1))) = mult(X2,mult(ld(X0,X0),ld(X1,X1))),
inference(forward_demodulation,[],[f1230,f30]) ).
fof(f1246,plain,
! [X2,X3,X0,X1] : ld(mult(X1,X0),mult(X3,mult(X1,X2))) = mult(X1,mult(ld(X1,mult(X1,ld(rd(X0,X2),ld(X1,X3)))),ld(X2,X2))),
inference(backward_demodulation,[],[f746,f1237]) ).
fof(f1249,plain,
! [X2,X3,X0,X1] : ld(mult(X1,X0),mult(X3,mult(X1,X2))) = mult(X1,mult(ld(rd(X0,X2),ld(X1,X3)),ld(X2,X2))),
inference(forward_demodulation,[],[f1246,f2]) ).
fof(f1251,plain,
! [X2,X3,X0,X1] : ld(mult(X1,X0),mult(X3,mult(X1,X2))) = mult(X1,ld(X0,mult(ld(X1,X3),X2))),
inference(forward_demodulation,[],[f1249,f127]) ).
fof(f1543,plain,
! [X2,X3,X0,X1] : mult(X1,mult(X3,X2)) = mult(mult(X3,X0),mult(X3,ld(X0,mult(ld(X3,X1),X2)))),
inference(superposition,[],[f1,f1251]) ).
fof(f2049,plain,
! [X2,X0,X1] : mult(X1,mult(X0,X2)) = mult(mult(X0,X0),mult(ld(X0,X1),X2)),
inference(superposition,[],[f1543,f1]) ).
fof(f2146,plain,
! [X2,X0,X1] : mult(mult(X0,X1),mult(X0,X2)) = mult(mult(X0,X0),mult(X1,X2)),
inference(superposition,[],[f2049,f2]) ).
fof(f2207,plain,
$false,
inference(backward_subsumption_resolution,[],[f7,f2146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP754-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n016.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 10:47:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 10.72/2.21 % (2435530)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.72/2.21 % (2435540)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=220396795:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.72/2.21 % (2435541)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3814547882:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.72/2.21 % (2435536)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=3908220669:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.72/2.21 % (2435537)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1267688938:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.72/2.21 % (2435539)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3136304886:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.72/2.21 % (2435535)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=3886830339:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.72/2.21 % (2435538)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=597086688:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.72/2.21 % (2435538)Instruction limit reached!
% 10.72/2.21 % (2435538)------------------------------
% 10.72/2.21 % (2435538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435538)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435538)Termination reason: Instruction limit
% 10.72/2.21 % (2435538)Termination phase: Saturation
% 10.72/2.21 % (2435538)Time elapsed: 0.080 s
% 10.72/2.21 % (2435538)Peak memory usage: 89 MB
% 10.72/2.21 % (2435538)Instructions burned: 137 (million)
% 10.72/2.21 % (2435539)Instruction limit reached!
% 10.72/2.21 % (2435539)------------------------------
% 10.72/2.21 % (2435539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435539)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435539)Termination reason: Instruction limit
% 10.72/2.21 % (2435539)Termination phase: Saturation
% 10.72/2.21 % (2435539)Time elapsed: 0.105 s
% 10.72/2.21 % (2435539)Peak memory usage: 89 MB
% 10.72/2.21 % (2435539)Instructions burned: 183 (million)
% 10.72/2.21 % (2435540)Instruction limit reached!
% 10.72/2.21 % (2435540)------------------------------
% 10.72/2.21 % (2435540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435540)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435540)Termination reason: Instruction limit
% 10.72/2.21 % (2435540)Termination phase: Saturation
% 10.72/2.21 % (2435540)Time elapsed: 0.167 s
% 10.72/2.21 % (2435540)Peak memory usage: 91 MB
% 10.72/2.21 % (2435540)Instructions burned: 258 (million)
% 10.72/2.21 % (2435549)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=4133365886:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 10.72/2.21 % (2435550)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1562677072:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 10.72/2.21 % (2435551)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=547378504:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.72/2.21 % (2435551)Instruction limit reached!
% 10.72/2.21 % (2435551)------------------------------
% 10.72/2.21 % (2435551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435551)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435551)Termination reason: Instruction limit
% 10.72/2.21 % (2435551)Termination phase: Saturation
% 10.72/2.21 % (2435551)Time elapsed: 0.118 s
% 10.72/2.21 % (2435551)Peak memory usage: 90 MB
% 10.72/2.21 % (2435551)Instructions burned: 217 (million)
% 10.72/2.21 % (2435555)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=1143034577: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)
% 10.72/2.21 % (2435541)Instruction limit reached!
% 10.72/2.21 % (2435541)------------------------------
% 10.72/2.21 % (2435541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435541)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435541)Termination reason: Instruction limit
% 10.72/2.21 % (2435541)Termination phase: Saturation
% 10.72/2.21 % (2435541)Time elapsed: 0.673 s
% 10.72/2.21 % (2435541)Peak memory usage: 101 MB
% 10.72/2.21 % (2435541)Instructions burned: 1188 (million)
% 10.72/2.21 % (2435555)Instruction limit reached!
% 10.72/2.21 % (2435555)------------------------------
% 10.72/2.21 % (2435555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435555)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435555)Termination reason: Instruction limit
% 10.72/2.21 % (2435555)Termination phase: Saturation
% 10.72/2.21 % (2435555)Time elapsed: 0.202 s
% 10.72/2.21 % (2435555)Peak memory usage: 94 MB
% 10.72/2.21 % (2435555)Instructions burned: 318 (million)
% 10.72/2.21 % (2435557)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=1887668631:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 10.72/2.21 % (2435558)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2063368085:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2991 on theBenchmark for (2991ds/2836Mi)
% 10.72/2.21 % (2435549)First to succeed.
% 10.72/2.21 % (2435549)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2435530"
% 10.72/2.21 % (2435549)Refutation found. Thanks to Tanya!
% 10.72/2.21 % SZS status Unsatisfiable for theBenchmark
% 10.72/2.21 % SZS output start Proof for theBenchmark
% See solution above
% 10.72/2.21 % (2435549)------------------------------
% 10.72/2.21 % (2435549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.72/2.21 % (2435549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.72/2.21 % (2435549)CaDiCaL version: 2.1.3
% 10.72/2.21 % (2435549)Termination reason: Refutation
% 10.72/2.21 % (2435549)Time elapsed: 0.889 s
% 10.72/2.21 % (2435549)Peak memory usage: 138 MB
% 10.72/2.21 % (2435549)Instructions burned: 1761 (million)
% 10.72/2.21 % (2435549)------------------------------
% 10.72/2.21 % (2435549)------------------------------
% 10.72/2.21 % (2435530)Success in time 1.466 s
% 10.72/2.21 % Vampire exiting
%------------------------------------------------------------------------------