%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG001-4 : 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 : n006.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 12:35:03 PM UTC 2026
% Result : Unsatisfiable 4.18s 1.57s
% Output : Refutation 4.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 26 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 27 ( 14 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f12,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X1,X2)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| sum(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f18,axiom,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X2)
| ~ sum(X0,X3,X2)
| X1 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
fof(f20,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
fof(f38,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X1,X3)
| ~ product(X0,X3,X4)
| sum(X2,X2,X4) ),
inference(factoring,[],[f12]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sum(X0,X1,X0)
| additive_identity = X1 ),
inference(resolution,[],[f18,f2]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| ~ sum(X1,X1,X1)
| sum(X2,X2,X2) ),
inference(factoring,[],[f38]) ).
fof(f358,plain,
! [X0,X1] :
( ~ sum(X0,X0,X0)
| sum(multiply(X1,X0),multiply(X1,X0),multiply(X1,X0)) ),
inference(resolution,[],[f131,f3]) ).
fof(f2196,plain,
! [X0] : sum(multiply(X0,additive_identity),multiply(X0,additive_identity),multiply(X0,additive_identity)),
inference(resolution,[],[f358,f2]) ).
fof(f4163,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(resolution,[],[f2196,f61]) ).
fof(f4215,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(superposition,[],[f3,f4163]) ).
fof(f4242,plain,
$false,
inference(resolution,[],[f4215,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:57:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 4.18/1.57 % (3425845)Input is clausal, will run a generic CNF schedule.
% 4.18/1.57 % (3425851)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3877115530:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.18/1.57 % (3425850)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=4159054033:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.18/1.57 % (3425852)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=245115774:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.18/1.57 % (3425854)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1387615767:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.18/1.57 % (3425856)dis-21_1_sil=8000:lcm=predicate:random_seed=459364091: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)
% 4.18/1.57 % (3425853)lrs+10_1_sil=8000:sp=occurrence:random_seed=3929782613:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.18/1.57 % (3425855)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1855066948:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.18/1.57 % (3425856)Instruction limit reached!
% 4.18/1.57 % (3425856)------------------------------
% 4.18/1.57 % (3425856)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.57 % (3425856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.57 % (3425856)CaDiCaL version: 2.1.3
% 4.18/1.57 % (3425856)Termination reason: Instruction limit
% 4.18/1.57 % (3425856)Termination phase: Saturation
% 4.18/1.57 % (3425856)Time elapsed: 0.058 s
% 4.18/1.57 % (3425856)Peak memory usage: 88 MB
% 4.18/1.57 % (3425856)Instructions burned: 119 (million)
% 4.18/1.57 % (3425854)Instruction limit reached!
% 4.18/1.57 % (3425854)------------------------------
% 4.18/1.57 % (3425854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.57 % (3425854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.57 % (3425854)CaDiCaL version: 2.1.3
% 4.18/1.57 % (3425854)Termination reason: Instruction limit
% 4.18/1.57 % (3425854)Termination phase: Saturation
% 4.18/1.57 % (3425854)Time elapsed: 0.062 s
% 4.18/1.57 % (3425854)Peak memory usage: 87 MB
% 4.18/1.57 % (3425854)Instructions burned: 114 (million)
% 4.18/1.57 % (3425853)Instruction limit reached!
% 4.18/1.57 % (3425853)------------------------------
% 4.18/1.57 % (3425853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.57 % (3425853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.57 % (3425853)CaDiCaL version: 2.1.3
% 4.18/1.57 % (3425853)Termination reason: Instruction limit
% 4.18/1.57 % (3425853)Termination phase: Saturation
% 4.18/1.57 % (3425853)Time elapsed: 0.066 s
% 4.18/1.57 % (3425853)Peak memory usage: 87 MB
% 4.18/1.57 % (3425853)Instructions burned: 107 (million)
% 4.18/1.57 % (3425855)First to succeed.
% 4.18/1.57 % (3425855)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3425845"
% 4.18/1.57 % (3425865)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1733604588: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)
% 4.18/1.57 % (3425864)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=4156656167:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 4.18/1.57 % (3425864)Refutation not found, incomplete strategy
% 4.18/1.57 % (3425864)------------------------------
% 4.18/1.57 % (3425864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.57 % (3425864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.57 % (3425864)CaDiCaL version: 2.1.3
% 4.18/1.57 % (3425864)Termination reason: Refutation not found, incomplete strategy
% 4.18/1.57 % (3425864)Time elapsed: 0.001 s
% 4.18/1.57 % (3425864)Peak memory usage: 87 MB
% 4.18/1.57 % (3425864)Instructions burned: 1 (million)
% 4.18/1.57 % (3425866)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=737791779:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.18/1.57 % (3425865)Instruction limit reached!
% 4.18/1.57 % (3425865)------------------------------
% 4.18/1.57 % (3425865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.57 % (3425865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.57 % (3425865)CaDiCaL version: 2.1.3
% 4.18/1.57 % (3425865)Termination reason: Instruction limit
% 4.18/1.57 % (3425865)Termination phase: Saturation
% 4.18/1.57 % (3425865)Time elapsed: 0.106 s
% 4.18/1.57 % (3425865)Peak memory usage: 89 MB
% 4.18/1.57 % (3425865)Instructions burned: 190 (million)
% 4.18/1.57 % (3425855)Refutation found. Thanks to Tanya!
% 4.18/1.57 % SZS status Unsatisfiable for theBenchmark
% 4.18/1.57 % SZS output start Proof for theBenchmark
% See solution above
% 4.18/1.57 % (3425855)------------------------------
% 4.18/1.57 % (3425855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.18/1.57 % (3425855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.18/1.57 % (3425855)CaDiCaL version: 2.1.3
% 4.18/1.57 % (3425855)Termination reason: Refutation
% 4.18/1.57 % (3425855)Time elapsed: 0.080 s
% 4.18/1.57 % (3425855)Peak memory usage: 89 MB
% 4.18/1.57 % (3425855)Instructions burned: 123 (million)
% 4.18/1.57 % (3425855)------------------------------
% 4.18/1.57 % (3425855)------------------------------
% 4.18/1.57 % (3425845)Success in time 0.513 s
% 4.18/1.58 % Vampire exiting
%------------------------------------------------------------------------------