%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 10:12:14 AM UTC 2026
% Result : Unsatisfiable 0.16s 1.61s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of formulae : 13 ( 10 unt; 0 def)
% Number of atoms : 21 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 12 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : product(identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
fof(f5,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X2,X3,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X4,X5)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
fof(f8,axiom,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
fof(f9,axiom,
product(c,a,result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_with_a) ).
fof(f10,negated_conjecture,
~ product(c,b,result),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product_with_b) ).
fof(f11,plain,
~ product(multiply(c,identity),b,result),
inference(unit_resulting_resolution,[],[f5,f3,f1,f10]) ).
fof(f15,plain,
product(identity,a,b),
inference(unit_resulting_resolution,[],[f7,f1,f8]) ).
fof(f43,plain,
~ product(identity,b,a),
inference(unit_resulting_resolution,[],[f6,f9,f3,f11]) ).
fof(f51,plain,
~ product(identity,a,b),
inference(unit_resulting_resolution,[],[f5,f1,f1,f43]) ).
fof(f62,plain,
$false,
inference(forward_subsumption_resolution,[],[f51,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP045-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:21:02 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.16/1.61 % (2357521)Input is clausal, will run a generic CNF schedule.
% 0.16/1.61 % (2357527)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4209063699:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.16/1.61 % (2357529)lrs+10_1_sil=8000:sp=occurrence:random_seed=359827790:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.16/1.61 % (2357531)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=667475321:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.16/1.61 % (2357532)dis-21_1_sil=8000:lcm=predicate:random_seed=144886061: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)
% 0.16/1.61 % (2357528)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4102805575:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.16/1.61 % (2357530)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2095165263:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.16/1.61 % (2357526)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=988952005:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.16/1.61 % (2357529)Refutation not found, incomplete strategy
% 0.16/1.61 % (2357529)------------------------------
% 0.16/1.61 % (2357529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357529)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357529)Termination reason: Refutation not found, incomplete strategy
% 0.16/1.61 % (2357529)Time elapsed: 0.002 s
% 0.16/1.61 % (2357529)Peak memory usage: 88 MB
% 0.16/1.61 % (2357529)Instructions burned: 1 (million)
% 0.16/1.61 % (2357532)Instruction limit reached!
% 0.16/1.61 % (2357532)------------------------------
% 0.16/1.61 % (2357532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357532)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357532)Termination reason: Instruction limit
% 0.16/1.61 % (2357532)Termination phase: Saturation
% 0.16/1.61 % (2357532)Time elapsed: 0.059 s
% 0.16/1.61 % (2357532)Peak memory usage: 88 MB
% 0.16/1.61 % (2357532)Instructions burned: 117 (million)
% 0.16/1.61 % (2357530)Instruction limit reached!
% 0.16/1.61 % (2357530)------------------------------
% 0.16/1.61 % (2357530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357530)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357530)Termination reason: Instruction limit
% 0.16/1.61 % (2357530)Termination phase: Saturation
% 0.16/1.61 % (2357530)Time elapsed: 0.063 s
% 0.16/1.61 % (2357530)Peak memory usage: 88 MB
% 0.16/1.61 % (2357530)Instructions burned: 115 (million)
% 0.16/1.61 % (2357531)Instruction limit reached!
% 0.16/1.61 % (2357531)------------------------------
% 0.16/1.61 % (2357531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357531)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357531)Termination reason: Instruction limit
% 0.16/1.61 % (2357531)Termination phase: Saturation
% 0.16/1.61 % (2357531)Time elapsed: 0.108 s
% 0.16/1.61 % (2357531)Peak memory usage: 88 MB
% 0.16/1.61 % (2357531)Instructions burned: 181 (million)
% 0.16/1.61 % (2357540)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=1679584580:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.16/1.61 % (2357541)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=910847867:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 0.16/1.61 % (2357541)First to succeed.
% 0.16/1.61 % (2357541)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2357521"
% 0.16/1.61 % (2357529)------------------------------
% 0.16/1.61 % (2357529)------------------------------
% 0.16/1.61 % (2357542)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2073942152:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.16/1.61 % (2357540)Instruction limit reached!
% 0.16/1.61 % (2357540)------------------------------
% 0.16/1.61 % (2357540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357540)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357540)Termination reason: Instruction limit
% 0.16/1.61 % (2357540)Termination phase: Saturation
% 0.16/1.61 % (2357540)Time elapsed: 0.096 s
% 0.16/1.61 % (2357540)Peak memory usage: 89 MB
% 0.16/1.61 % (2357540)Instructions burned: 144 (million)
% 0.16/1.61 % (2357527)Also succeeded, but the first one will report.
% 0.16/1.61 % (2357542)Instruction limit reached!
% 0.16/1.61 % (2357542)------------------------------
% 0.16/1.61 % (2357542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357542)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357542)Termination reason: Instruction limit
% 0.16/1.61 % (2357542)Termination phase: Saturation
% 0.16/1.61 % (2357542)Time elapsed: 0.124 s
% 0.16/1.61 % (2357542)Peak memory usage: 88 MB
% 0.16/1.61 % (2357542)Instructions burned: 220 (million)
% 0.16/1.61 % (2357545)lrs+10_64_to=lpo:sil=8000:random_seed=2460875944:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.16/1.61 % (2357541)Refutation found. Thanks to Tanya!
% 0.16/1.61 % SZS status Unsatisfiable for theBenchmark
% 0.16/1.61 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.61 % (2357541)------------------------------
% 0.16/1.61 % (2357541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.61 % (2357541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.61 % (2357541)CaDiCaL version: 2.1.3
% 0.16/1.61 % (2357541)Termination reason: Refutation
% 0.16/1.61 % (2357541)Time elapsed: 0.003 s
% 0.16/1.61 % (2357541)Peak memory usage: 88 MB
% 0.16/1.61 % (2357541)Instructions burned: 3 (million)
% 0.16/1.61 % (2357541)------------------------------
% 0.16/1.61 % (2357541)------------------------------
% 0.16/1.61 % (2357521)Success in time 0.644 s
% 0.16/1.61 % Vampire exiting
%------------------------------------------------------------------------------