%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG004-3 : 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 12:35:04 PM UTC 2026
% Result : Unsatisfiable 5.71s 1.75s
% Output : Refutation 5.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 18 ( 14 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 29 ( 16 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f20,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2)
| ~ sum(X0,X4,X5)
| sum(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f24,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X0,X5,X6)
| ~ product(X0,X3,X4)
| ~ sum(X1,X3,X5)
| ~ product(X0,X1,X2)
| sum(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
fof(f26,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X5,X1,X6)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ product(X0,X1,X2)
| sum(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
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,axiom,
! [X0] : product(additive_identity,X0,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity1) ).
fof(f31,axiom,
! [X0] : product(X0,additive_identity,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_identity2) ).
fof(f32,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f33,axiom,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b_inverse) ).
fof(f34,negated_conjecture,
~ equalish(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f46,plain,
~ sum(additive_identity,d,c),
inference(unit_resulting_resolution,[],[f28,f34,f13]) ).
fof(f260,plain,
sum(multiply(additive_inverse(a),b),d,additive_identity),
inference(unit_resulting_resolution,[],[f24,f15,f33,f18,f31]) ).
fof(f669,plain,
sum(c,multiply(additive_inverse(a),b),additive_identity),
inference(unit_resulting_resolution,[],[f26,f32,f15,f18,f30]) ).
fof(f2206,plain,
~ sum(multiply(additive_inverse(a),b),d,additive_identity),
inference(unit_resulting_resolution,[],[f20,f46,f14,f669]) ).
fof(f2570,plain,
$false,
inference(forward_subsumption_resolution,[],[f2206,f260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 22:57:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 5.71/1.75 % (3426266)Input is clausal, will run a generic CNF schedule.
% 5.71/1.75 % (3426272)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4009548194:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.71/1.75 % (3426276)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2166888902:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.71/1.75 % (3426271)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=1535672721:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.71/1.75 % (3426275)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3422770441:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.71/1.75 % (3426274)lrs+10_1_sil=8000:sp=occurrence:random_seed=1397127048:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.71/1.75 % (3426273)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3794487790:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.71/1.75 % (3426277)dis-21_1_sil=8000:lcm=predicate:random_seed=1945690865: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)
% 5.71/1.75 % (3426275)Instruction limit reached!
% 5.71/1.75 % (3426275)------------------------------
% 5.71/1.75 % (3426275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426275)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426275)Termination reason: Instruction limit
% 5.71/1.75 % (3426275)Termination phase: Saturation
% 5.71/1.75 % (3426275)Time elapsed: 0.059 s
% 5.71/1.75 % (3426275)Peak memory usage: 87 MB
% 5.71/1.75 % (3426275)Instructions burned: 116 (million)
% 5.71/1.75 % (3426274)Instruction limit reached!
% 5.71/1.75 % (3426274)------------------------------
% 5.71/1.75 % (3426274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426274)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426274)Termination reason: Instruction limit
% 5.71/1.75 % (3426274)Termination phase: Saturation
% 5.71/1.75 % (3426274)Time elapsed: 0.065 s
% 5.71/1.75 % (3426274)Peak memory usage: 88 MB
% 5.71/1.75 % (3426274)Instructions burned: 109 (million)
% 5.71/1.75 % (3426277)Instruction limit reached!
% 5.71/1.75 % (3426277)------------------------------
% 5.71/1.75 % (3426277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426277)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426277)Termination reason: Instruction limit
% 5.71/1.75 % (3426277)Termination phase: Saturation
% 5.71/1.75 % (3426277)Time elapsed: 0.061 s
% 5.71/1.75 % (3426277)Peak memory usage: 87 MB
% 5.71/1.75 % (3426277)Instructions burned: 119 (million)
% 5.71/1.75 % (3426276)Instruction limit reached!
% 5.71/1.75 % (3426276)------------------------------
% 5.71/1.75 % (3426276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426276)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426276)Termination reason: Instruction limit
% 5.71/1.75 % (3426276)Termination phase: Saturation
% 5.71/1.75 % (3426276)Time elapsed: 0.105 s
% 5.71/1.75 % (3426276)Peak memory usage: 89 MB
% 5.71/1.75 % (3426276)Instructions burned: 181 (million)
% 5.71/1.75 % (3426285)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=3240342828:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.71/1.75 % (3426287)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1294446194:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.71/1.75 % (3426286)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2290920214: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)
% 5.71/1.75 % (3426288)lrs+10_64_to=lpo:sil=8000:random_seed=1288900930:i=126:bd=preordered_2997 on theBenchmark for (2997ds/126Mi)
% 5.71/1.75 % (3426285)Instruction limit reached!
% 5.71/1.75 % (3426285)------------------------------
% 5.71/1.75 % (3426285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426285)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426285)Termination reason: Instruction limit
% 5.71/1.75 % (3426285)Termination phase: Saturation
% 5.71/1.75 % (3426285)Time elapsed: 0.091 s
% 5.71/1.75 % (3426285)Peak memory usage: 89 MB
% 5.71/1.75 % (3426285)Instructions burned: 143 (million)
% 5.71/1.75 % (3426286)Instruction limit reached!
% 5.71/1.75 % (3426286)------------------------------
% 5.71/1.75 % (3426286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426286)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426286)Termination reason: Instruction limit
% 5.71/1.75 % (3426286)Termination phase: Saturation
% 5.71/1.75 % (3426286)Time elapsed: 0.098 s
% 5.71/1.75 % (3426286)Peak memory usage: 88 MB
% 5.71/1.75 % (3426286)Instructions burned: 189 (million)
% 5.71/1.75 % (3426288)Instruction limit reached!
% 5.71/1.75 % (3426288)------------------------------
% 5.71/1.75 % (3426288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426288)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426288)Termination reason: Instruction limit
% 5.71/1.75 % (3426288)Termination phase: Saturation
% 5.71/1.75 % (3426288)Time elapsed: 0.075 s
% 5.71/1.75 % (3426288)Peak memory usage: 89 MB
% 5.71/1.75 % (3426288)Instructions burned: 126 (million)
% 5.71/1.75 % (3426287)Instruction limit reached!
% 5.71/1.75 % (3426287)------------------------------
% 5.71/1.75 % (3426287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426287)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426287)Termination reason: Instruction limit
% 5.71/1.75 % (3426287)Termination phase: Saturation
% 5.71/1.75 % (3426287)Time elapsed: 0.131 s
% 5.71/1.75 % (3426287)Peak memory usage: 89 MB
% 5.71/1.75 % (3426287)Instructions burned: 219 (million)
% 5.71/1.75 % (3426293)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3015632493:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 5.71/1.75 % (3426272)First to succeed.
% 5.71/1.75 % (3426272)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3426266"
% 5.71/1.75 % (3426294)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2501313804:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 5.71/1.75 % (3426295)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=2442272365:i=3394:sd=4:ss=included:sgt=64_2995 on theBenchmark for (2995ds/3394Mi)
% 5.71/1.75 % (3426296)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2259926197:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2995 on theBenchmark for (2995ds/106Mi)
% 5.71/1.75 % (3426293)Instruction limit reached!
% 5.71/1.75 % (3426293)------------------------------
% 5.71/1.75 % (3426293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426293)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426293)Termination reason: Instruction limit
% 5.71/1.75 % (3426293)Termination phase: Saturation
% 5.71/1.75 % (3426293)Time elapsed: 0.080 s
% 5.71/1.75 % (3426293)Peak memory usage: 87 MB
% 5.71/1.75 % (3426293)Instructions burned: 194 (million)
% 5.71/1.75 % (3426296)Instruction limit reached!
% 5.71/1.75 % (3426296)------------------------------
% 5.71/1.75 % (3426296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426296)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426296)Termination reason: Instruction limit
% 5.71/1.75 % (3426296)Termination phase: Saturation
% 5.71/1.75 % (3426296)Time elapsed: 0.059 s
% 5.71/1.75 % (3426296)Peak memory usage: 89 MB
% 5.71/1.75 % (3426296)Instructions burned: 107 (million)
% 5.71/1.75 % (3426294)Instruction limit reached!
% 5.71/1.75 % (3426294)------------------------------
% 5.71/1.75 % (3426294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426294)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426294)Termination reason: Instruction limit
% 5.71/1.75 % (3426294)Termination phase: Saturation
% 5.71/1.75 % (3426294)Time elapsed: 0.102 s
% 5.71/1.75 % (3426294)Peak memory usage: 89 MB
% 5.71/1.75 % (3426294)Instructions burned: 158 (million)
% 5.71/1.75 % (3426272)Refutation found. Thanks to Tanya!
% 5.71/1.75 % SZS status Unsatisfiable for theBenchmark
% 5.71/1.75 % SZS output start Proof for theBenchmark
% See solution above
% 5.71/1.75 % (3426272)------------------------------
% 5.71/1.75 % (3426272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.71/1.75 % (3426272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.71/1.75 % (3426272)CaDiCaL version: 2.1.3
% 5.71/1.75 % (3426272)Termination reason: Refutation
% 5.71/1.75 % (3426272)Time elapsed: 0.463 s
% 5.71/1.75 % (3426272)Peak memory usage: 131 MB
% 5.71/1.75 % (3426272)Instructions burned: 1197 (million)
% 5.71/1.75 % (3426272)------------------------------
% 5.71/1.75 % (3426272)------------------------------
% 5.71/1.75 % (3426266)Success in time 0.724 s
% 5.71/1.75 % Vampire exiting
%------------------------------------------------------------------------------