%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:11:36 PM UTC 2026
% Result : Unsatisfiable 3.66s 1.50s
% Output : Refutation 3.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 15 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( ~ less(X2,X0)
| ~ less(X0,X1)
| less(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less) ).
fof(f13,axiom,
! [X2,X0,X1] :
( equalish(multiply(X0,X2),multiply(X1,X2))
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_preserved_over_times) ).
fof(f14,axiom,
! [X0,X1] :
( ~ less(X0,X1)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_and_equal) ).
fof(f15,axiom,
! [X0,X1] :
( less(X1,X0)
| less(X0,X1)
| equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
fof(f16,axiom,
! [X0] : ~ less(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',number_not_less_than_itself) ).
fof(f18,axiom,
! [X2,X0,X1] :
( less(multiply(X0,X2),multiply(X1,X2))
| equalish(X2,n0)
| ~ less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_lemma) ).
fof(f19,axiom,
~ less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_less_than_a) ).
fof(f20,axiom,
less(multiply(b,c),multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
fof(f21,negated_conjecture,
~ equalish(c,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_0) ).
fof(f27,plain,
~ equalish(multiply(b,c),multiply(a,c)),
inference(resolution,[],[f20,f14]) ).
fof(f34,plain,
! [X0] :
( ~ less(multiply(a,c),X0)
| less(multiply(b,c),X0) ),
inference(resolution,[],[f7,f20]) ).
fof(f58,plain,
~ equalish(b,a),
inference(resolution,[],[f13,f27]) ).
fof(f97,plain,
! [X0] :
( less(multiply(b,c),multiply(X0,c))
| equalish(c,n0)
| ~ less(a,X0) ),
inference(resolution,[],[f34,f18]) ).
fof(f101,plain,
! [X0] :
( less(multiply(b,c),multiply(X0,c))
| ~ less(a,X0) ),
inference(forward_subsumption_resolution,[],[f97,f21]) ).
fof(f102,plain,
~ less(a,b),
inference(resolution,[],[f101,f16]) ).
fof(f107,plain,
( less(b,a)
| equalish(b,a) ),
inference(resolution,[],[f102,f15]) ).
fof(f110,plain,
equalish(b,a),
inference(forward_subsumption_resolution,[],[f107,f19]) ).
fof(f111,plain,
$false,
inference(forward_subsumption_resolution,[],[f110,f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM027-1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.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 18:40:16 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 3.66/1.50 % (1097009)Input is clausal, will run a generic CNF schedule.
% 3.66/1.50 % (1097020)dis-21_1_sil=8000:lcm=predicate:random_seed=359402855: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)
% 3.66/1.50 % (1097017)lrs+10_1_sil=8000:sp=occurrence:random_seed=647912420:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.66/1.50 % (1097015)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=964858934:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.66/1.50 % (1097018)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1710308428:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.66/1.50 % (1097016)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3524747916:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.66/1.50 % (1097014)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=2819893619:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.66/1.50 % (1097019)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2664847106:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.66/1.50 % (1097020)Instruction limit reached!
% 3.66/1.50 % (1097020)------------------------------
% 3.66/1.50 % (1097020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.50 % (1097020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.50 % (1097020)CaDiCaL version: 2.1.3
% 3.66/1.50 % (1097020)Termination reason: Instruction limit
% 3.66/1.50 % (1097020)Termination phase: Saturation
% 3.66/1.50 % (1097020)Time elapsed: 0.044 s
% 3.66/1.50 % (1097020)Peak memory usage: 89 MB
% 3.66/1.50 % (1097020)Instructions burned: 119 (million)
% 3.66/1.50 % (1097017)First to succeed.
% 3.66/1.50 % (1097017)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1097009"
% 3.66/1.50 % (1097019)Also succeeded, but the first one will report.
% 3.66/1.50 % (1097018)Also succeeded, but the first one will report.
% 3.66/1.50 % (1097028)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=309397715:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.66/1.50 % (1097028)Also succeeded, but the first one will report.
% 3.66/1.50 % (1097017)Refutation found. Thanks to Tanya!
% 3.66/1.50 % SZS status Unsatisfiable for theBenchmark
% 3.66/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.66/1.50 % (1097017)------------------------------
% 3.66/1.50 % (1097017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.66/1.50 % (1097017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.66/1.50 % (1097017)CaDiCaL version: 2.1.3
% 3.66/1.50 % (1097017)Termination reason: Refutation
% 3.66/1.50 % (1097017)Time elapsed: 0.004 s
% 3.66/1.50 % (1097017)Peak memory usage: 88 MB
% 3.66/1.50 % (1097017)Instructions burned: 3 (million)
% 3.66/1.50 % (1097017)------------------------------
% 3.66/1.50 % (1097017)------------------------------
% 3.66/1.50 % (1097009)Success in time 0.439 s
% 3.66/1.50 % Vampire exiting
%------------------------------------------------------------------------------