%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:35:05 PM UTC 2026
% Result : Unsatisfiable 0.23s 1.92s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 26 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 32 ( 19 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ sum(X2,X4,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
fof(f18,axiom,
! [X2,X0,X1] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_lemma1) ).
fof(f21,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f22,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f23,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c) ).
fof(f24,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f25,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( ~ sum(X3,X1,aPb_S_IaPc)
| ~ sum(X2,X0,bS_Ic)
| ~ product(a,X0,X1)
| ~ product(a,X2,X3) ),
inference(resolution,[],[f13,f25]) ).
fof(f82,plain,
! [X0,X1] :
( ~ product(a,X1,additive_inverse(aPc))
| ~ sum(X0,X1,bS_Ic)
| ~ product(a,X0,aPb) ),
inference(resolution,[],[f50,f24]) ).
fof(f159,plain,
! [X0,X1] :
( ~ sum(X0,additive_inverse(X1),bS_Ic)
| ~ product(a,X0,aPb)
| ~ product(a,X1,aPc) ),
inference(resolution,[],[f82,f18]) ).
fof(f171,plain,
( ~ product(a,b,aPb)
| ~ product(a,c,aPc) ),
inference(resolution,[],[f159,f21]) ).
fof(f172,plain,
~ product(a,c,aPc),
inference(forward_subsumption_resolution,[],[f171,f22]) ).
fof(f173,plain,
$false,
inference(forward_subsumption_resolution,[],[f172,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 % Computer : n011.cluster.edu
% 0.15/0.44 % Model : x86_64 x86_64
% 0.15/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.44 % Memory : 8046.5625MB
% 0.15/0.44 % OS : Linux 6.8.0-71-generic
% 0.15/0.44 % CPULimit : 300
% 0.15/0.44 % WCLimit : 300
% 0.15/0.44 % DateTime : Sun Sep 27 22:58:00 UTC 2026
% 0.15/0.44 % CPUTime :
% 0.15/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.23/1.91 % (2860447)Input is clausal, will run a generic CNF schedule.
% 0.23/1.91 % (2860458)dis-21_1_sil=8000:lcm=predicate:random_seed=2106456743: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)
% 0.23/1.91 % (2860453)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1461482074:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.23/1.91 % (2860457)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2848172491:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.23/1.91 % (2860452)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=1341842865:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.23/1.91 % (2860455)lrs+10_1_sil=8000:sp=occurrence:random_seed=2654704591:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.23/1.91 % (2860456)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=282170988:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.23/1.91 % (2860457)First to succeed.
% 0.23/1.91 % (2860457)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2860447"
% 0.23/1.91 % (2860454)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1698074027:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.23/1.91 % (2860458)Instruction limit reached!
% 0.23/1.91 % (2860458)------------------------------
% 0.23/1.91 % (2860458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.91 % (2860458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.91 % (2860458)CaDiCaL version: 2.1.3
% 0.23/1.91 % (2860458)Termination reason: Instruction limit
% 0.23/1.91 % (2860458)Termination phase: Saturation
% 0.23/1.91 % (2860458)Time elapsed: 0.107 s
% 0.23/1.91 % (2860458)Peak memory usage: 88 MB
% 0.23/1.91 % (2860458)Instructions burned: 118 (million)
% 0.23/1.91 % (2860455)Instruction limit reached!
% 0.23/1.91 % (2860455)------------------------------
% 0.23/1.91 % (2860455)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.91 % (2860455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.91 % (2860455)CaDiCaL version: 2.1.3
% 0.23/1.91 % (2860455)Termination reason: Instruction limit
% 0.23/1.91 % (2860455)Termination phase: Saturation
% 0.23/1.91 % (2860455)Time elapsed: 0.109 s
% 0.23/1.91 % (2860455)Peak memory usage: 89 MB
% 0.23/1.91 % (2860455)Instructions burned: 107 (million)
% 0.23/1.91 % (2860456)Instruction limit reached!
% 0.23/1.91 % (2860456)------------------------------
% 0.23/1.91 % (2860456)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.91 % (2860456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.91 % (2860456)CaDiCaL version: 2.1.3
% 0.23/1.91 % (2860456)Termination reason: Instruction limit
% 0.23/1.91 % (2860456)Termination phase: Saturation
% 0.23/1.91 % (2860456)Time elapsed: 0.109 s
% 0.23/1.91 % (2860456)Peak memory usage: 88 MB
% 0.23/1.91 % (2860456)Instructions burned: 116 (million)
% 0.23/1.91 % (2860466)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=2599832759:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.23/1.92 % (2860468)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=365334342:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 0.23/1.92 % (2860467)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3383869252: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)
% 0.23/1.92 % (2860457)Refutation found. Thanks to Tanya!
% 0.23/1.92 % SZS status Unsatisfiable for theBenchmark
% 0.23/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/1.92 % (2860457)------------------------------
% 0.23/1.92 % (2860457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.23/1.92 % (2860457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/1.92 % (2860457)CaDiCaL version: 2.1.3
% 0.23/1.92 % (2860457)Termination reason: Refutation
% 0.23/1.92 % (2860457)Time elapsed: 0.013 s
% 0.23/1.92 % (2860457)Peak memory usage: 88 MB
% 0.23/1.92 % (2860457)Instructions burned: 11 (million)
% 0.23/1.92 % (2860457)------------------------------
% 0.23/1.92 % (2860457)------------------------------
% 0.23/1.92 % (2860447)Success in time 0.652 s
% 0.23/1.92 % Vampire exiting
%------------------------------------------------------------------------------