%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG006-2 : 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 : n020.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 4.46s 2.12s
% Output : Refutation 4.46s
% 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 : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,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(f29,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(f32,axiom,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f33,axiom,
product(a,b,aPb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f34,axiom,
product(a,c,aPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c) ).
fof(f35,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f36,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(f58,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,[],[f22,f36]) ).
fof(f87,plain,
! [X0,X1] :
( ~ product(a,X1,additive_inverse(aPc))
| ~ sum(X0,X1,bS_Ic)
| ~ product(a,X0,aPb) ),
inference(resolution,[],[f58,f35]) ).
fof(f143,plain,
! [X0,X1] :
( ~ product(a,X1,aPc)
| ~ product(a,X0,aPb)
| ~ sum(X0,additive_inverse(X1),bS_Ic) ),
inference(resolution,[],[f87,f29]) ).
fof(f1104,plain,
! [X0] :
( ~ product(a,X0,aPb)
| ~ sum(X0,additive_inverse(c),bS_Ic) ),
inference(resolution,[],[f143,f34]) ).
fof(f1112,plain,
~ sum(b,additive_inverse(c),bS_Ic),
inference(resolution,[],[f1104,f33]) ).
fof(f1120,plain,
$false,
inference(forward_subsumption_resolution,[],[f1112,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 % Computer : n020.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.09/0.48 % CPULimit : 300
% 0.09/0.48 % WCLimit : 300
% 0.09/0.48 % DateTime : Sun Sep 27 22:59:05 UTC 2026
% 0.09/0.49 % CPUTime :
% 0.09/0.49 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.55 Running first-order theorem proving
% 0.09/0.55 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
% 4.46/2.12 % (3866336)Input is clausal, will run a generic CNF schedule.
% 4.46/2.12 % (3866346)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2487987478:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.46/2.12 % (3866346)First to succeed.
% 4.46/2.12 % (3866346)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3866336"
% 4.46/2.12 % (3866344)lrs+10_1_sil=8000:sp=occurrence:random_seed=372296114:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.46/2.12 % (3866341)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=223729974:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.46/2.12 % (3866342)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1312875878:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.46/2.12 % (3866343)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2570497340:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.46/2.12 % (3866347)dis-21_1_sil=8000:lcm=predicate:random_seed=840716657: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)
% 4.46/2.12 % (3866345)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3435256239:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.46/2.12 % (3866344)Instruction limit reached!
% 4.46/2.12 % (3866344)------------------------------
% 4.46/2.12 % (3866344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.46/2.12 % (3866344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/2.12 % (3866344)CaDiCaL version: 2.1.3
% 4.46/2.12 % (3866344)Termination reason: Instruction limit
% 4.46/2.12 % (3866344)Termination phase: Saturation
% 4.46/2.12 % (3866344)Time elapsed: 0.102 s
% 4.46/2.12 % (3866344)Peak memory usage: 89 MB
% 4.46/2.12 % (3866344)Instructions burned: 107 (million)
% 4.46/2.12 % (3866345)Instruction limit reached!
% 4.46/2.12 % (3866345)------------------------------
% 4.46/2.12 % (3866345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.46/2.12 % (3866345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/2.12 % (3866345)CaDiCaL version: 2.1.3
% 4.46/2.12 % (3866345)Termination reason: Instruction limit
% 4.46/2.12 % (3866345)Termination phase: Saturation
% 4.46/2.12 % (3866345)Time elapsed: 0.104 s
% 4.46/2.12 % (3866345)Peak memory usage: 88 MB
% 4.46/2.12 % (3866345)Instructions burned: 114 (million)
% 4.46/2.12 % (3866347)Instruction limit reached!
% 4.46/2.12 % (3866347)------------------------------
% 4.46/2.12 % (3866347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.46/2.12 % (3866347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/2.12 % (3866347)CaDiCaL version: 2.1.3
% 4.46/2.12 % (3866347)Termination reason: Instruction limit
% 4.46/2.12 % (3866347)Termination phase: Saturation
% 4.46/2.12 % (3866347)Time elapsed: 0.106 s
% 4.46/2.12 % (3866347)Peak memory usage: 88 MB
% 4.46/2.12 % (3866347)Instructions burned: 117 (million)
% 4.46/2.12 % (3866346)Refutation found. Thanks to Tanya!
% 4.46/2.12 % SZS status Unsatisfiable for theBenchmark
% 4.46/2.12 % SZS output start Proof for theBenchmark
% See solution above
% 4.46/2.12 % (3866346)------------------------------
% 4.46/2.12 % (3866346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.46/2.12 % (3866346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.46/2.12 % (3866346)CaDiCaL version: 2.1.3
% 4.46/2.12 % (3866346)Termination reason: Refutation
% 4.46/2.12 % (3866346)Time elapsed: 0.043 s
% 4.46/2.12 % (3866346)Peak memory usage: 88 MB
% 4.46/2.12 % (3866346)Instructions burned: 88 (million)
% 4.46/2.12 % (3866346)------------------------------
% 4.46/2.12 % (3866346)------------------------------
% 4.46/2.12 % (3866336)Success in time 0.467 s
% 4.46/2.12 % Vampire exiting
%------------------------------------------------------------------------------