%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP698-1 : 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 : 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 10:15:58 AM UTC 2026
% Result : Unsatisfiable 10.32s 2.27s
% Output : Refutation 10.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
fof(f5,axiom,
! [X0] : mult(X0,unit) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
fof(f7,axiom,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X0),mult(X0,X2)) = mult(X0,mult(mult(mult(X1,X0),X0),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
fof(f9,negated_conjecture,
mult(a,mult(b,c)) != mult(rd(mult(a,b),a),mult(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f39,plain,
! [X2,X0,X1] : mult(mult(X1,X2),X1) = rd(mult(X1,mult(mult(mult(X2,X1),X1),X0)),mult(X1,X0)),
inference(superposition,[],[f4,f7]) ).
fof(f100,plain,
! [X2,X0,X1] : mult(mult(X1,rd(X0,X1)),X1) = rd(mult(X1,mult(mult(X0,X1),X2)),mult(X1,X2)),
inference(superposition,[],[f39,f3]) ).
fof(f546,plain,
! [X2,X0,X1] : mult(mult(X1,rd(rd(X0,X1),X1)),X1) = rd(mult(X1,mult(X0,X2)),mult(X1,X2)),
inference(superposition,[],[f100,f3]) ).
fof(f566,plain,
! [X0,X1] : mult(mult(X1,rd(X0,X1)),X1) = rd(mult(X1,mult(X0,X1)),mult(X1,unit)),
inference(superposition,[],[f100,f5]) ).
fof(f588,plain,
! [X0,X1] : mult(mult(X1,rd(X0,X1)),X1) = rd(mult(X1,mult(X0,X1)),X1),
inference(forward_demodulation,[],[f566,f5]) ).
fof(f625,plain,
! [X0,X1] : mult(mult(X1,rd(rd(X0,X1),X1)),X1) = rd(mult(X1,X0),X1),
inference(superposition,[],[f588,f3]) ).
fof(f654,plain,
! [X2,X0,X1] : rd(mult(X1,mult(X0,X2)),mult(X1,X2)) = rd(mult(X1,X0),X1),
inference(backward_demodulation,[],[f546,f625]) ).
fof(f726,plain,
! [X2,X0,X1] : mult(X2,mult(X1,X0)) = mult(rd(mult(X2,X1),X2),mult(X2,X0)),
inference(superposition,[],[f3,f654]) ).
fof(f727,plain,
$false,
inference(backward_subsumption_resolution,[],[f9,f726]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP698-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n001.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 10:42:15 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 10.32/2.27 % (3370443)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.32/2.27 % (3370453)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=355753602:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.32/2.27 % (3370450)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3545848710:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.32/2.27 % (3370451)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=107041627:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.32/2.27 % (3370448)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=1555772065:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.32/2.27 % (3370452)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1067501165:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.32/2.27 % (3370449)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=3290259069:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.32/2.27 % (3370454)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2418480677:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.32/2.27 % (3370451)Instruction limit reached!
% 10.32/2.27 % (3370451)------------------------------
% 10.32/2.27 % (3370451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370451)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370451)Termination reason: Instruction limit
% 10.32/2.27 % (3370451)Termination phase: Saturation
% 10.32/2.27 % (3370451)Time elapsed: 0.081 s
% 10.32/2.27 % (3370451)Peak memory usage: 88 MB
% 10.32/2.27 % (3370451)Instructions burned: 137 (million)
% 10.32/2.27 % (3370452)Instruction limit reached!
% 10.32/2.27 % (3370452)------------------------------
% 10.32/2.27 % (3370452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370452)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370452)Termination reason: Instruction limit
% 10.32/2.27 % (3370452)Termination phase: Saturation
% 10.32/2.27 % (3370452)Time elapsed: 0.100 s
% 10.32/2.27 % (3370452)Peak memory usage: 89 MB
% 10.32/2.27 % (3370452)Instructions burned: 182 (million)
% 10.32/2.27 % (3370453)Instruction limit reached!
% 10.32/2.27 % (3370453)------------------------------
% 10.32/2.27 % (3370453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370453)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370453)Termination reason: Instruction limit
% 10.32/2.27 % (3370453)Termination phase: Saturation
% 10.32/2.27 % (3370453)Time elapsed: 0.195 s
% 10.32/2.27 % (3370453)Peak memory usage: 90 MB
% 10.32/2.27 % (3370453)Instructions burned: 257 (million)
% 10.32/2.27 % (3370465)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2496556809:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 10.32/2.27 % (3370466)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=644452517:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 10.32/2.27 % (3370467)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2275474912:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.32/2.27 % (3370467)Instruction limit reached!
% 10.32/2.27 % (3370467)------------------------------
% 10.32/2.27 % (3370467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370467)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370467)Termination reason: Instruction limit
% 10.32/2.27 % (3370467)Termination phase: Saturation
% 10.32/2.27 % (3370467)Time elapsed: 0.117 s
% 10.32/2.27 % (3370467)Peak memory usage: 90 MB
% 10.32/2.27 % (3370467)Instructions burned: 215 (million)
% 10.32/2.27 % (3370538)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=305589994:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 10.32/2.27 % (3370454)Instruction limit reached!
% 10.32/2.27 % (3370454)------------------------------
% 10.32/2.27 % (3370454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370454)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370454)Termination reason: Instruction limit
% 10.32/2.27 % (3370454)Termination phase: Saturation
% 10.32/2.27 % (3370454)Time elapsed: 0.645 s
% 10.32/2.27 % (3370454)Peak memory usage: 98 MB
% 10.32/2.27 % (3370454)Instructions burned: 1187 (million)
% 10.32/2.27 % (3370538)Instruction limit reached!
% 10.32/2.27 % (3370538)------------------------------
% 10.32/2.27 % (3370538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370538)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370538)Termination reason: Instruction limit
% 10.32/2.27 % (3370538)Termination phase: Saturation
% 10.32/2.27 % (3370538)Time elapsed: 0.198 s
% 10.32/2.27 % (3370538)Peak memory usage: 93 MB
% 10.32/2.27 % (3370538)Instructions burned: 318 (million)
% 10.32/2.27 % (3370583)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=1972902350:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 10.32/2.27 % (3370465)First to succeed.
% 10.32/2.27 % (3370465)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3370443"
% 10.32/2.27 % (3370627)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=2258338689:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2990 on theBenchmark for (2990ds/2836Mi)
% 10.32/2.27 % (3370465)Refutation found. Thanks to Tanya!
% 10.32/2.27 % SZS status Unsatisfiable for theBenchmark
% 10.32/2.27 % SZS output start Proof for theBenchmark
% See solution above
% 10.32/2.27 % (3370465)------------------------------
% 10.32/2.27 % (3370465)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.27 % (3370465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.27 % (3370465)CaDiCaL version: 2.1.3
% 10.32/2.27 % (3370465)Termination reason: Refutation
% 10.32/2.27 % (3370465)Time elapsed: 0.757 s
% 10.32/2.27 % (3370465)Peak memory usage: 131 MB
% 10.32/2.27 % (3370465)Instructions burned: 1155 (million)
% 10.32/2.27 % (3370465)------------------------------
% 10.32/2.27 % (3370465)------------------------------
% 10.32/2.27 % (3370443)Success in time 1.407 s
% 10.32/2.27 % Vampire exiting
%------------------------------------------------------------------------------