%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG037-1 : 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 : 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 12:35:14 PM UTC 2026
% Result : Unsatisfiable 0.08s 1.12s
% Output : Refutation 0.08s
% 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/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f4,axiom,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
fof(f5,axiom,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f12,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/sandbox/benchmark/theBenchmark.p',distributivity1) ).
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,
product(a,b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f19,axiom,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_inverse_times_b) ).
fof(f20,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
fof(f26,plain,
~ sum(add(c,d),additive_identity,additive_identity),
inference(unit_resulting_resolution,[],[f7,f4,f2,f20]) ).
fof(f66,plain,
product(a,b,add(d,multiply(a,additive_identity))),
inference(unit_resulting_resolution,[],[f13,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(f2157,plain,
~ product(a,b,add(d,multiply(a,additive_identity))),
inference(unit_resulting_resolution,[],[f12,f3,f5,f19,f1380]) ).
fof(f2166,plain,
$false,
inference(forward_subsumption_resolution,[],[f2157,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.33 % Computer : n012.cluster.edu
% 0.04/0.33 % Model : x86_64 x86_64
% 0.04/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.33 % Memory : 8046.5625MB
% 0.04/0.33 % OS : Linux 6.8.0-71-generic
% 0.04/0.33 % CPULimit : 300
% 0.04/0.33 % WCLimit : 300
% 0.04/0.33 % DateTime : Sun Sep 27 23:01:04 UTC 2026
% 0.04/0.33 % CPUTime :
% 0.04/0.33 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.35 Running first-order theorem proving
% 0.04/0.35 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
% 0.08/1.12 % (2859089)Input is clausal, will run a generic CNF schedule.
% 0.08/1.12 % (2859099)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2355135965:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.08/1.12 % (2859096)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1601466562:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.08/1.12 % (2859098)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3737733216:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.08/1.12 % (2859097)lrs+10_1_sil=8000:sp=occurrence:random_seed=2688794104:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.08/1.12 % (2859094)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=1683947262:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.08/1.12 % (2859095)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2912125138:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.08/1.12 % (2859100)dis-21_1_sil=8000:lcm=predicate:random_seed=72314468: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)
% 0.08/1.12 % (2859100)Instruction limit reached!
% 0.08/1.12 % (2859100)------------------------------
% 0.08/1.12 % (2859100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859100)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859100)Termination reason: Instruction limit
% 0.08/1.12 % (2859100)Termination phase: Saturation
% 0.08/1.12 % (2859100)Time elapsed: 0.032 s
% 0.08/1.12 % (2859100)Peak memory usage: 88 MB
% 0.08/1.12 % (2859100)Instructions burned: 118 (million)
% 0.08/1.12 % (2859098)Instruction limit reached!
% 0.08/1.12 % (2859098)------------------------------
% 0.08/1.12 % (2859098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859098)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859098)Termination reason: Instruction limit
% 0.08/1.12 % (2859098)Termination phase: Saturation
% 0.08/1.12 % (2859098)Time elapsed: 0.033 s
% 0.08/1.12 % (2859098)Peak memory usage: 88 MB
% 0.08/1.12 % (2859098)Instructions burned: 117 (million)
% 0.08/1.12 % (2859097)Instruction limit reached!
% 0.08/1.12 % (2859097)------------------------------
% 0.08/1.12 % (2859097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859097)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859097)Termination reason: Instruction limit
% 0.08/1.12 % (2859097)Termination phase: Saturation
% 0.08/1.12 % (2859097)Time elapsed: 0.037 s
% 0.08/1.12 % (2859097)Peak memory usage: 88 MB
% 0.08/1.12 % (2859097)Instructions burned: 110 (million)
% 0.08/1.12 % (2859099)Instruction limit reached!
% 0.08/1.12 % (2859099)------------------------------
% 0.08/1.12 % (2859099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859099)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859099)Termination reason: Instruction limit
% 0.08/1.12 % (2859099)Termination phase: Saturation
% 0.08/1.12 % (2859099)Time elapsed: 0.059 s
% 0.08/1.12 % (2859099)Peak memory usage: 88 MB
% 0.08/1.12 % (2859099)Instructions burned: 182 (million)
% 0.08/1.12 % (2859109)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2291252243:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2998 on theBenchmark for (2998ds/189Mi)
% 0.08/1.12 % (2859110)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=4224357673:st=4:i=219:sd=3:ss=axioms_2998 on theBenchmark for (2998ds/219Mi)
% 0.08/1.12 % (2859108)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=2706908571:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 0.08/1.12 % (2859109)First to succeed.
% 0.08/1.12 % (2859109)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2859089"
% 0.08/1.12 % (2859111)lrs+10_64_to=lpo:sil=8000:random_seed=4126164526:i=126:bd=preordered_2998 on theBenchmark for (2998ds/126Mi)
% 0.08/1.12 % (2859108)Instruction limit reached!
% 0.08/1.12 % (2859108)------------------------------
% 0.08/1.12 % (2859108)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859108)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859108)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859108)Termination reason: Instruction limit
% 0.08/1.12 % (2859108)Termination phase: Saturation
% 0.08/1.12 % (2859108)Time elapsed: 0.049 s
% 0.08/1.12 % (2859108)Peak memory usage: 88 MB
% 0.08/1.12 % (2859108)Instructions burned: 143 (million)
% 0.08/1.12 % (2859110)Instruction limit reached!
% 0.08/1.12 % (2859110)------------------------------
% 0.08/1.12 % (2859110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859110)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859110)Termination reason: Instruction limit
% 0.08/1.12 % (2859110)Termination phase: Saturation
% 0.08/1.12 % (2859110)Time elapsed: 0.068 s
% 0.08/1.12 % (2859110)Peak memory usage: 89 MB
% 0.08/1.12 % (2859110)Instructions burned: 219 (million)
% 0.08/1.12 % (2859111)Instruction limit reached!
% 0.08/1.12 % (2859111)------------------------------
% 0.08/1.12 % (2859111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859111)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859111)Termination reason: Instruction limit
% 0.08/1.12 % (2859111)Termination phase: Saturation
% 0.08/1.12 % (2859111)Time elapsed: 0.042 s
% 0.08/1.12 % (2859111)Peak memory usage: 88 MB
% 0.08/1.12 % (2859111)Instructions burned: 126 (million)
% 0.08/1.12 % (2859116)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1010989769:avsq=on:i=194:fgj=on:bd=preordered_2996 on theBenchmark for (2996ds/194Mi)
% 0.08/1.12 % (2859109)Refutation found. Thanks to Tanya!
% 0.08/1.12 % SZS status Unsatisfiable for theBenchmark
% 0.08/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/1.12 % (2859109)------------------------------
% 0.08/1.12 % (2859109)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.08/1.12 % (2859109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/1.12 % (2859109)CaDiCaL version: 2.1.3
% 0.08/1.12 % (2859109)Termination reason: Refutation
% 0.08/1.12 % (2859109)Time elapsed: 0.025 s
% 0.08/1.12 % (2859109)Peak memory usage: 89 MB
% 0.08/1.12 % (2859109)Instructions burned: 83 (million)
% 0.08/1.12 % (2859109)------------------------------
% 0.08/1.12 % (2859109)------------------------------
% 0.08/1.12 % (2859089)Success in time 0.466 s
% 0.08/1.12 % Vampire exiting
%------------------------------------------------------------------------------