%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG001-5 : 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 : n012.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 5.37s 1.49s
% Output : Refutation 5.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 13 ( 9 unt; 0 def)
% Number of atoms : 24 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 26 ( 15 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,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(f13,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f14,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f15,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f18,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f19,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X2,X3,X5)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition1) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X2,X4,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X5,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f30,negated_conjecture,
~ product(a,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiplicative_identity_axiom) ).
fof(f34,plain,
~ equalish(multiply(a,additive_identity),additive_identity),
inference(unit_resulting_resolution,[],[f12,f15,f30]) ).
fof(f60,plain,
~ sum(multiply(a,additive_identity),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f28,f14,f34]) ).
fof(f155,plain,
! [X0] : ~ sum(multiply(a,additive_identity),X0,X0),
inference(unit_resulting_resolution,[],[f19,f18,f18,f60]) ).
fof(f784,plain,
$false,
inference(unit_resulting_resolution,[],[f24,f15,f15,f13,f15,f155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG001-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 22:57:19 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 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
% 5.37/1.49 % (2852851)Input is clausal, will run a generic CNF schedule.
% 5.37/1.49 % (2852881)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2193974565:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.37/1.49 % (2852881)Instruction limit reached!
% 5.37/1.49 % (2852881)------------------------------
% 5.37/1.49 % (2852881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852881)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852881)Termination reason: Instruction limit
% 5.37/1.49 % (2852881)Termination phase: Saturation
% 5.37/1.49 % (2852881)Time elapsed: 0.037 s
% 5.37/1.49 % (2852881)Peak memory usage: 87 MB
% 5.37/1.49 % (2852881)Instructions burned: 185 (million)
% 5.37/1.49 % (2852880)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2485886530:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.37/1.49 % (2852877)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1818077398:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.37/1.49 % (2852879)lrs+10_1_sil=8000:sp=occurrence:random_seed=2572904312:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.37/1.49 % (2852882)dis-21_1_sil=8000:lcm=predicate:random_seed=3904338136: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)
% 5.37/1.49 % (2852876)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=539743060:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.37/1.49 % (2852878)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2320634378:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.37/1.49 % (2852880)Instruction limit reached!
% 5.37/1.49 % (2852880)------------------------------
% 5.37/1.49 % (2852880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852880)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852880)Termination reason: Instruction limit
% 5.37/1.49 % (2852880)Termination phase: Saturation
% 5.37/1.49 % (2852880)Time elapsed: 0.051 s
% 5.37/1.49 % (2852880)Peak memory usage: 87 MB
% 5.37/1.49 % (2852880)Instructions burned: 115 (million)
% 5.37/1.49 % (2852882)Instruction limit reached!
% 5.37/1.49 % (2852882)------------------------------
% 5.37/1.49 % (2852882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852882)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852882)Termination reason: Instruction limit
% 5.37/1.49 % (2852882)Termination phase: Saturation
% 5.37/1.49 % (2852882)Time elapsed: 0.055 s
% 5.37/1.49 % (2852882)Peak memory usage: 88 MB
% 5.37/1.49 % (2852882)Instructions burned: 118 (million)
% 5.37/1.49 % (2852879)Instruction limit reached!
% 5.37/1.49 % (2852879)------------------------------
% 5.37/1.49 % (2852879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852879)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852879)Termination reason: Instruction limit
% 5.37/1.49 % (2852879)Termination phase: Saturation
% 5.37/1.49 % (2852879)Time elapsed: 0.057 s
% 5.37/1.49 % (2852879)Peak memory usage: 87 MB
% 5.37/1.49 % (2852879)Instructions burned: 107 (million)
% 5.37/1.49 % (2852885)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=2539741628:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 5.37/1.49 % (2852885)Refutation not found, incomplete strategy
% 5.37/1.49 % (2852885)------------------------------
% 5.37/1.49 % (2852885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852885)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852885)Termination reason: Refutation not found, incomplete strategy
% 5.37/1.49 % (2852885)Time elapsed: 0.001 s
% 5.37/1.49 % (2852885)Peak memory usage: 88 MB
% 5.37/1.49 % (2852894)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1486495954:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.37/1.49 % (2852893)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=737126895: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)
% 5.37/1.49 % (2852893)First to succeed.
% 5.37/1.49 % (2852893)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2852851"
% 5.37/1.49 % (2852895)lrs+10_64_to=lpo:sil=8000:random_seed=3389503364:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.37/1.49 % (2852894)Instruction limit reached!
% 5.37/1.49 % (2852894)------------------------------
% 5.37/1.49 % (2852894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852894)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852894)Termination reason: Instruction limit
% 5.37/1.49 % (2852894)Termination phase: Saturation
% 5.37/1.49 % (2852894)Time elapsed: 0.072 s
% 5.37/1.49 % (2852894)Peak memory usage: 89 MB
% 5.37/1.49 % (2852894)Instructions burned: 221 (million)
% 5.37/1.49 % (2852895)Instruction limit reached!
% 5.37/1.49 % (2852895)------------------------------
% 5.37/1.49 % (2852895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852895)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852895)Termination reason: Instruction limit
% 5.37/1.49 % (2852895)Termination phase: Saturation
% 5.37/1.49 % (2852895)Time elapsed: 0.065 s
% 5.37/1.49 % (2852895)Peak memory usage: 88 MB
% 5.37/1.49 % (2852895)Instructions burned: 127 (million)
% 5.37/1.49 % (2852885)------------------------------
% 5.37/1.49 % (2852885)------------------------------
% 5.37/1.49 % (2852906)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2859539874:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.37/1.49 % (2852893)Refutation found. Thanks to Tanya!
% 5.37/1.49 % SZS status Unsatisfiable for theBenchmark
% 5.37/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 5.37/1.49 % (2852893)------------------------------
% 5.37/1.49 % (2852893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.37/1.49 % (2852893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.37/1.49 % (2852893)CaDiCaL version: 2.1.3
% 5.37/1.49 % (2852893)Termination reason: Refutation
% 5.37/1.49 % (2852893)Time elapsed: 0.013 s
% 5.37/1.49 % (2852893)Peak memory usage: 88 MB
% 5.37/1.49 % (2852893)Instructions burned: 24 (million)
% 5.37/1.49 % (2852893)------------------------------
% 5.37/1.49 % (2852893)------------------------------
% 5.37/1.49 % (2852851)Success in time 0.72 s
% 5.37/1.49 % Vampire exiting
%------------------------------------------------------------------------------