%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG005-1 : 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 : n001.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 12:35:04 PM UTC 2026
% Result : Unsatisfiable 7.63s 2.49s
% Output : Refutation 7.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 33 ( 19 ~; 14 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 35 !; 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(f4,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f7,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(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X4,X5)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( sum(X2,X4,X6)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ product(X5,X1,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ sum(X2,X4,X6)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
fof(f18,axiom,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f19,axiom,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
fof(f20,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_id) ).
fof(f26,plain,
~ sum(add(c,d),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f7,f4,f2,f20]) ).
fof(f87,plain,
product(a,b,add(d,multiply(additive_identity,b))),
inference(unit_resulting_resolution,[],[f15,f2,f4,f3,f18]) ).
fof(f829,plain,
! [X0] : ~ sum(add(c,d),X0,X0),
inference(unit_resulting_resolution,[],[f7,f6,f6,f26]) ).
fof(f1380,plain,
! [X0] : ~ sum(c,add(d,X0),X0),
inference(unit_resulting_resolution,[],[f8,f4,f4,f829]) ).
fof(f2161,plain,
~ product(a,b,add(d,multiply(additive_identity,b))),
inference(unit_resulting_resolution,[],[f14,f3,f5,f19,f1380]) ).
fof(f2167,plain,
$false,
inference(forward_subsumption_resolution,[],[f2161,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.47 % Computer : n001.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 27 23:04:01 UTC 2026
% 0.20/0.48 % CPUTime :
% 0.20/0.48 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.53 Running first-order theorem proving
% 0.26/0.53 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
% 7.63/2.49 % (4066705)Input is clausal, will run a generic CNF schedule.
% 7.63/2.49 % (4066721)lrs+10_1_sil=8000:sp=occurrence:random_seed=1777557164:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 7.63/2.49 % (4066721)Instruction limit reached!
% 7.63/2.49 % (4066721)------------------------------
% 7.63/2.49 % (4066721)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066721)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066721)Termination reason: Instruction limit
% 7.63/2.49 % (4066721)Termination phase: Saturation
% 7.63/2.49 % (4066721)Time elapsed: 0.053 s
% 7.63/2.49 % (4066721)Peak memory usage: 88 MB
% 7.63/2.49 % (4066721)Instructions burned: 108 (million)
% 7.63/2.49 % (4066722)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2771760214:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 7.63/2.49 % (4066719)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3232600448:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 7.63/2.49 % (4066718)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=1880664373:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 7.63/2.49 % (4066720)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=912901524:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 7.63/2.49 % (4066724)dis-21_1_sil=8000:lcm=predicate:random_seed=572585369: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)
% 7.63/2.49 % (4066723)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2306720007:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 7.63/2.49 % (4066722)Instruction limit reached!
% 7.63/2.49 % (4066722)------------------------------
% 7.63/2.49 % (4066722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066722)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066722)Termination reason: Instruction limit
% 7.63/2.49 % (4066722)Termination phase: Saturation
% 7.63/2.49 % (4066722)Time elapsed: 0.092 s
% 7.63/2.49 % (4066722)Peak memory usage: 87 MB
% 7.63/2.49 % (4066722)Instructions burned: 115 (million)
% 7.63/2.49 % (4066724)Instruction limit reached!
% 7.63/2.49 % (4066724)------------------------------
% 7.63/2.49 % (4066724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066724)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066724)Termination reason: Instruction limit
% 7.63/2.49 % (4066724)Termination phase: Saturation
% 7.63/2.49 % (4066724)Time elapsed: 0.102 s
% 7.63/2.49 % (4066724)Peak memory usage: 88 MB
% 7.63/2.49 % (4066724)Instructions burned: 118 (million)
% 7.63/2.49 % (4066723)Instruction limit reached!
% 7.63/2.49 % (4066723)------------------------------
% 7.63/2.49 % (4066723)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066723)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066723)Termination reason: Instruction limit
% 7.63/2.49 % (4066723)Termination phase: Saturation
% 7.63/2.49 % (4066723)Time elapsed: 0.163 s
% 7.63/2.49 % (4066723)Peak memory usage: 88 MB
% 7.63/2.49 % (4066723)Instructions burned: 181 (million)
% 7.63/2.49 % (4066726)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=2985056086:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 7.63/2.49 % (4066726)Instruction limit reached!
% 7.63/2.49 % (4066726)------------------------------
% 7.63/2.49 % (4066726)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066726)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066726)Termination reason: Instruction limit
% 7.63/2.49 % (4066726)Termination phase: Saturation
% 7.63/2.49 % (4066726)Time elapsed: 0.078 s
% 7.63/2.49 % (4066726)Peak memory usage: 89 MB
% 7.63/2.49 % (4066726)Instructions burned: 145 (million)
% 7.63/2.49 % (4066733)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2878087154: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)
% 7.63/2.49 % (4066734)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=40186798:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 7.63/2.49 % (4066733)First to succeed.
% 7.63/2.49 % (4066733)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4066705"
% 7.63/2.49 % (4066735)lrs+10_64_to=lpo:sil=8000:random_seed=3538444662:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 7.63/2.49 % (4066735)Instruction limit reached!
% 7.63/2.49 % (4066735)------------------------------
% 7.63/2.49 % (4066735)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066735)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066735)Termination reason: Instruction limit
% 7.63/2.49 % (4066735)Termination phase: Saturation
% 7.63/2.49 % (4066735)Time elapsed: 0.122 s
% 7.63/2.49 % (4066735)Peak memory usage: 88 MB
% 7.63/2.49 % (4066735)Instructions burned: 126 (million)
% 7.63/2.49 % (4066734)Instruction limit reached!
% 7.63/2.49 % (4066734)------------------------------
% 7.63/2.49 % (4066734)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.49 % (4066734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.49 % (4066734)CaDiCaL version: 2.1.3
% 7.63/2.49 % (4066734)Termination reason: Instruction limit
% 7.63/2.49 % (4066734)Termination phase: Saturation
% 7.63/2.49 % (4066734)Time elapsed: 0.211 s
% 7.63/2.49 % (4066734)Peak memory usage: 89 MB
% 7.63/2.49 % (4066734)Instructions burned: 219 (million)
% 7.63/2.49 % (4066737)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=855013887:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 7.63/2.49 % (4066733)Refutation found. Thanks to Tanya!
% 7.63/2.49 % SZS status Unsatisfiable for theBenchmark
% 7.63/2.49 % SZS output start Proof for theBenchmark
% See solution above
% 7.63/2.50 % (4066733)------------------------------
% 7.63/2.50 % (4066733)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.63/2.50 % (4066733)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.63/2.50 % (4066733)CaDiCaL version: 2.1.3
% 7.63/2.50 % (4066733)Termination reason: Refutation
% 7.63/2.50 % (4066733)Time elapsed: 0.039 s
% 7.63/2.50 % (4066733)Peak memory usage: 89 MB
% 7.63/2.50 % (4066733)Instructions burned: 84 (million)
% 7.63/2.50 % (4066733)------------------------------
% 7.63/2.50 % (4066733)------------------------------
% 7.63/2.50 % (4066705)Success in time 0.934 s
% 7.63/2.50 % Vampire exiting
%------------------------------------------------------------------------------