%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP748-4 : 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 : n011.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 10:16:06 AM UTC 2026
% Result : Unsatisfiable 8.79s 2.28s
% Output : Refutation 8.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 43 ( 32 unt; 0 def)
% Number of atoms : 56 ( 55 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 4 ~; 13 |; 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f2,axiom,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f3,axiom,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f4,axiom,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f6,axiom,
! [X0] : mult(unit,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f7,axiom,
! [X2,X0,X1] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(f8,axiom,
! [X0,X1] : mult(mult(X0,X1),i(X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f11,axiom,
! [X0] : mult(i(X0),X0) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
fof(f12,plain,
! [X0] : unit = mult(i(X0),X0),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( mult(i(X0),mult(X0,X1)) = X1
| mult(X0,X1) = mult(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
fof(f14,negated_conjecture,
mult(mult(a,b),mult(c,a)) != mult(mult(a,mult(b,c)),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f23,plain,
! [X0,X1] : mult(i(X0),mult(mult(X0,X1),X0)) = mult(mult(unit,X1),X0),
inference(superposition,[],[f7,f12]) ).
fof(f24,plain,
! [X0,X1] : mult(X1,X0) = mult(i(X0),mult(mult(X0,X1),X0)),
inference(forward_demodulation,[],[f23,f6]) ).
fof(f85,plain,
! [X0,X1] : mult(mult(mult(X1,X0),X1),i(X1)) = mult(i(i(X1)),mult(mult(X0,X1),i(X1))),
inference(superposition,[],[f24,f24]) ).
fof(f98,plain,
! [X0,X1] : mult(i(i(X1)),X0) = mult(mult(mult(X1,X0),X1),i(X1)),
inference(forward_demodulation,[],[f85,f8]) ).
fof(f103,plain,
! [X0,X1] : mult(X1,X0) = mult(i(i(X1)),X0),
inference(forward_demodulation,[],[f98,f8]) ).
fof(f254,plain,
! [X0,X1] : rd(X0,X1) = mult(X0,i(X1)),
inference(superposition,[],[f8,f3]) ).
fof(f256,plain,
! [X2,X0,X1] : mult(rd(X0,X1),mult(mult(X1,X2),X1)) = mult(mult(X0,X2),X1),
inference(superposition,[],[f7,f3]) ).
fof(f436,plain,
! [X2,X0,X1] : mult(mult(X2,X1),X2) = ld(rd(X0,X2),mult(mult(X0,X1),X2)),
inference(superposition,[],[f2,f256]) ).
fof(f439,plain,
! [X0,X1] :
( mult(X1,X0) = ld(i(X1),X0)
| mult(X0,X1) = mult(X1,X0) ),
inference(superposition,[],[f2,f13]) ).
fof(f448,plain,
! [X2,X0,X1] : mult(mult(X1,ld(X2,X0)),X1) = ld(rd(X2,X1),mult(X0,X1)),
inference(superposition,[],[f436,f1]) ).
fof(f567,plain,
! [X0,X1] :
( mult(X0,mult(i(X0),X1)) = mult(mult(i(X0),X1),X0)
| mult(X0,mult(i(X0),X1)) = X1 ),
inference(superposition,[],[f2,f439]) ).
fof(f576,plain,
! [X0,X1] :
( mult(i(X0),mult(X0,X1)) = mult(mult(X0,X1),i(X0))
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(superposition,[],[f567,f103]) ).
fof(f614,plain,
! [X0,X1] :
( mult(i(X0),mult(X0,X1)) = rd(mult(X0,X1),X0)
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(forward_demodulation,[],[f576,f254]) ).
fof(f648,plain,
! [X0,X1] :
( mult(X0,rd(mult(X0,X1),X0)) = mult(rd(mult(X0,X1),X0),X0)
| mult(X0,X1) = mult(X0,rd(mult(X0,X1),X0))
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(superposition,[],[f567,f614]) ).
fof(f660,plain,
! [X0,X1] :
( rd(mult(X0,X1),X0) != X1
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(equality_factoring,[],[f614]) ).
fof(f668,plain,
! [X0,X1] :
( mult(X0,X1) = mult(X0,rd(mult(X0,X1),X0))
| mult(X0,X1) = mult(X0,rd(mult(X0,X1),X0))
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(forward_demodulation,[],[f648,f3]) ).
fof(f669,plain,
! [X0,X1] :
( mult(X0,X1) = mult(X0,rd(mult(X0,X1),X0))
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(duplicate_literal_removal,[],[f668]) ).
fof(f1746,plain,
! [X2,X0,X1] : mult(mult(X1,ld(mult(X0,X1),X2)),X1) = ld(X0,mult(X2,X1)),
inference(superposition,[],[f448,f4]) ).
fof(f1994,plain,
! [X0,X1] :
( ld(X0,mult(X0,X1)) = rd(mult(X0,X1),X0)
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(superposition,[],[f2,f669]) ).
fof(f2038,plain,
! [X0,X1] :
( rd(mult(X0,X1),X0) = X1
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(forward_demodulation,[],[f1994,f2]) ).
fof(f2058,plain,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
inference(forward_subsumption_resolution,[],[f2038,f660]) ).
fof(f2095,plain,
! [X0,X1] : i(X1) = mult(i(mult(X0,X1)),X0),
inference(superposition,[],[f2058,f8]) ).
fof(f2105,plain,
! [X0,X1] : mult(mult(X1,X0),X1) = mult(i(i(X1)),mult(X0,X1)),
inference(superposition,[],[f2058,f24]) ).
fof(f2115,plain,
! [X0,X1] : mult(X1,X0) = ld(i(X1),X0),
inference(superposition,[],[f2,f2058]) ).
fof(f2152,plain,
! [X0,X1] : mult(X1,mult(X0,X1)) = mult(mult(X1,X0),X1),
inference(forward_demodulation,[],[f2105,f103]) ).
fof(f2228,plain,
mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)),
inference(superposition,[],[f14,f2152]) ).
fof(f2716,plain,
! [X2,X0,X1] : ld(i(mult(X1,X0)),mult(X2,X1)) = mult(mult(X1,ld(i(X0),X2)),X1),
inference(superposition,[],[f1746,f2095]) ).
fof(f2730,plain,
! [X2,X0,X1] : ld(i(mult(X1,X0)),mult(X2,X1)) = mult(X1,mult(ld(i(X0),X2),X1)),
inference(forward_demodulation,[],[f2716,f2152]) ).
fof(f2784,plain,
! [X2,X0,X1] : ld(i(mult(X1,X0)),mult(X2,X1)) = mult(X1,mult(mult(X0,X2),X1)),
inference(forward_demodulation,[],[f2730,f2115]) ).
fof(f2816,plain,
! [X2,X0,X1] : mult(X1,mult(mult(X0,X2),X1)) = mult(mult(X1,X0),mult(X2,X1)),
inference(forward_demodulation,[],[f2784,f2115]) ).
fof(f2963,plain,
mult(a,mult(mult(b,c),a)) != mult(a,mult(mult(b,c),a)),
inference(superposition,[],[f2228,f2816]) ).
fof(f2999,plain,
$false,
inference(trivial_inequality_removal,[],[f2963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP748-4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:41:30 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.44 Running first-order theorem proving
% 0.18/0.44 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
% 7.37/2.13 % (2204918)Input is clausal, will run a generic CNF schedule.
% 7.37/2.13 % (2204936)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2048335964:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.37/2.13 % (2204932)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2701815323:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.37/2.13 % (2204935)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1539919539:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.37/2.13 % (2204937)dis-21_1_sil=8000:lcm=predicate:random_seed=710271528:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 7.37/2.13 % (2204934)lrs+10_1_sil=8000:sp=occurrence:random_seed=2980872126:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.37/2.13 % (2204931)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=60349351:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.37/2.13 % (2204937)Refutation not found, incomplete strategy
% 7.37/2.13 % (2204937)------------------------------
% 7.37/2.13 % (2204937)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.13 % (2204937)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.13 % (2204937)CaDiCaL version: 2.1.3
% 7.37/2.13 % (2204937)Termination reason: Refutation not found, incomplete strategy
% 7.37/2.13 % (2204937)Time elapsed: 0.002 s
% 7.37/2.13 % (2204937)Peak memory usage: 88 MB
% 7.37/2.13 % (2204933)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1898282819:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.37/2.13 % (2204936)Instruction limit reached!
% 7.37/2.13 % (2204936)------------------------------
% 7.37/2.13 % (2204936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.13 % (2204936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.13 % (2204936)CaDiCaL version: 2.1.3
% 7.37/2.13 % (2204936)Termination reason: Instruction limit
% 7.37/2.13 % (2204936)Termination phase: Saturation
% 7.37/2.13 % (2204936)Time elapsed: 0.147 s
% 7.37/2.13 % (2204936)Peak memory usage: 89 MB
% 7.37/2.13 % (2204936)Instructions burned: 180 (million)
% 7.37/2.13 % (2204934)Instruction limit reached!
% 7.37/2.13 % (2204934)------------------------------
% 7.37/2.13 % (2204934)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.13 % (2204934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.13 % (2204934)CaDiCaL version: 2.1.3
% 7.37/2.13 % (2204934)Termination reason: Instruction limit
% 7.37/2.13 % (2204934)Termination phase: Saturation
% 7.37/2.13 % (2204934)Time elapsed: 0.102 s
% 7.37/2.13 % (2204934)Peak memory usage: 88 MB
% 7.37/2.13 % (2204934)Instructions burned: 107 (million)
% 7.37/2.13 % (2204935)Instruction limit reached!
% 7.37/2.13 % (2204935)------------------------------
% 7.37/2.13 % (2204935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.13 % (2204935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.13 % (2204935)CaDiCaL version: 2.1.3
% 7.37/2.13 % (2204935)Termination reason: Instruction limit
% 7.37/2.13 % (2204935)Termination phase: Saturation
% 7.37/2.13 % (2204935)Time elapsed: 0.105 s
% 7.37/2.13 % (2204935)Peak memory usage: 88 MB
% 7.37/2.13 % (2204935)Instructions burned: 114 (million)
% 7.37/2.13 % (2204945)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2846936976:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 7.37/2.13 % (2204945)Refutation not found, incomplete strategy
% 7.37/2.13 % (2204945)------------------------------
% 7.37/2.13 % (2204945)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.37/2.13 % (2204945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.37/2.13 % (2204945)CaDiCaL version: 2.1.3
% 7.37/2.13 % (2204945)Termination reason: Refutation not found, incomplete strategy
% 7.37/2.13 % (2204945)Time elapsed: 0.001 s
% 7.37/2.13 % (2204945)Peak memory usage: 88 MB
% 7.37/2.13 % (2204946)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1172671902:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 8.79/2.28 % (2204947)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1127723357:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 8.79/2.28 % (2204947)Refutation not found, incomplete strategy
% 8.79/2.28 % (2204947)------------------------------
% 8.79/2.28 % (2204947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.28 % (2204947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.28 % (2204947)CaDiCaL version: 2.1.3
% 8.79/2.28 % (2204947)Termination reason: Refutation not found, incomplete strategy
% 8.79/2.28 % (2204947)Time elapsed: 0.002 s
% 8.79/2.28 % (2204947)Peak memory usage: 87 MB
% 8.79/2.28 % (2204946)Refutation not found, incomplete strategy
% 8.79/2.28 % (2204946)------------------------------
% 8.79/2.28 % (2204946)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.28 % (2204946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.28 % (2204946)CaDiCaL version: 2.1.3
% 8.79/2.28 % (2204946)Termination reason: Refutation not found, incomplete strategy
% 8.79/2.28 % (2204946)Time elapsed: 0.002 s
% 8.79/2.28 % (2204946)Peak memory usage: 88 MB
% 8.79/2.28 % (2204946)Instructions burned: 1 (million)
% 8.79/2.28 % (2204937)------------------------------
% 8.79/2.28 % (2204937)------------------------------
% 8.79/2.28 % (2204952)lrs+10_64_to=lpo:sil=8000:random_seed=1506961285:i=126:bd=preordered_2994 on theBenchmark for (2994ds/126Mi)
% 8.79/2.28 % (2204945)------------------------------
% 8.79/2.28 % (2204945)------------------------------
% 8.79/2.28 % (2204952)Instruction limit reached!
% 8.79/2.28 % (2204952)------------------------------
% 8.79/2.28 % (2204952)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.28 % (2204952)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.28 % (2204952)CaDiCaL version: 2.1.3
% 8.79/2.28 % (2204952)Termination reason: Instruction limit
% 8.79/2.28 % (2204952)Termination phase: Saturation
% 8.79/2.28 % (2204952)Time elapsed: 0.136 s
% 8.79/2.28 % (2204952)Peak memory usage: 89 MB
% 8.79/2.28 % (2204952)Instructions burned: 126 (million)
% 8.79/2.28 % (2204932)First to succeed.
% 8.79/2.28 % (2204932)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2204918"
% 8.79/2.28 % (2204947)------------------------------
% 8.79/2.28 % (2204947)------------------------------
% 8.79/2.28 % (2204946)------------------------------
% 8.79/2.28 % (2204946)------------------------------
% 8.79/2.28 % (2204955)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=831156236:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 8.79/2.28 % (2204956)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=497438880:i=157:gtg=all_2991 on theBenchmark for (2991ds/157Mi)
% 8.79/2.28 % (2204932)Refutation found. Thanks to Tanya!
% 8.79/2.28 % SZS status Unsatisfiable for theBenchmark
% 8.79/2.28 % SZS output start Proof for theBenchmark
% See solution above
% 8.79/2.28 % (2204932)------------------------------
% 8.79/2.28 % (2204932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.79/2.28 % (2204932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.79/2.28 % (2204932)CaDiCaL version: 2.1.3
% 8.79/2.28 % (2204932)Termination reason: Refutation
% 8.79/2.28 % (2204932)Time elapsed: 0.757 s
% 8.79/2.28 % (2204932)Peak memory usage: 132 MB
% 8.79/2.28 % (2204932)Instructions burned: 1317 (million)
% 8.79/2.28 % (2204932)------------------------------
% 8.79/2.28 % (2204932)------------------------------
% 8.79/2.28 % (2204918)Success in time 1.152 s
% 8.79/2.28 % Vampire exiting
%------------------------------------------------------------------------------