%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG039-1 : 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 : n007.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 12:35:15 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.47s
% Output : Refutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 34 unt; 0 def)
% Number of atoms : 55 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
fof(f17,axiom,
! [X2,X3,X0,X1] :
( ~ product(X0,X1,X2)
| ~ product(X0,X1,X3)
| X2 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
fof(f22,axiom,
! [X0] : add(X0,X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
fof(f23,plain,
! [X0] : additive_identity = add(X0,X0),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
fof(f26,axiom,
multiply(b,a) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
fof(f32,axiom,
! [X0,X1] : product(X0,multiply(X0,X1),multiply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
fof(f33,axiom,
! [X0,X1] : product(a,multiply(b,X0),multiply(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
fof(f40,axiom,
product(a,d,multiply(c,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
fof(f46,axiom,
! [X0] : product(multiply(X0,b),a,multiply(X0,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
fof(f55,axiom,
product(add(b,a),b,add(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
fof(f56,axiom,
product(add(b,a),a,add(d,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
fof(f59,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
fof(f61,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
fof(f70,plain,
! [X0] : product(a,d,multiply(X0,a)),
inference(superposition,[],[f33,f26]) ).
fof(f71,plain,
! [X0] : product(a,b,multiply(X0,b)),
inference(superposition,[],[f33,f24]) ).
fof(f94,plain,
product(a,d,a),
inference(superposition,[],[f70,f24]) ).
fof(f96,plain,
product(a,b,b),
inference(superposition,[],[f71,f24]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ product(X0,X1,X2)
| multiply(X0,X1) = X2 ),
inference(resolution,[],[f17,f3]) ).
fof(f127,plain,
! [X0] :
( ~ product(add(b,a),a,X0)
| add(d,a) = X0 ),
inference(resolution,[],[f17,f56]) ).
fof(f135,plain,
! [X0] :
( ~ product(a,d,X0)
| multiply(c,a) = X0 ),
inference(resolution,[],[f17,f40]) ).
fof(f140,plain,
! [X0] :
( ~ product(a,b,X0)
| c = X0 ),
inference(resolution,[],[f17,f59]) ).
fof(f158,plain,
! [X0] : c = multiply(X0,b),
inference(resolution,[],[f140,f71]) ).
fof(f161,plain,
b = c,
inference(resolution,[],[f140,f96]) ).
fof(f182,plain,
b != d,
inference(superposition,[],[f61,f161]) ).
fof(f198,plain,
! [X0] : b = multiply(X0,b),
inference(forward_demodulation,[],[f158,f161]) ).
fof(f287,plain,
! [X0] : multiply(X0,d) = multiply(multiply(X0,b),a),
inference(resolution,[],[f118,f46]) ).
fof(f290,plain,
add(b,c) = multiply(add(b,a),b),
inference(resolution,[],[f118,f55]) ).
fof(f335,plain,
b = add(b,c),
inference(forward_demodulation,[],[f290,f198]) ).
fof(f337,plain,
! [X0] : multiply(b,a) = multiply(X0,d),
inference(forward_demodulation,[],[f287,f198]) ).
fof(f346,plain,
b = add(b,b),
inference(forward_demodulation,[],[f335,f161]) ).
fof(f348,plain,
! [X0] : d = multiply(X0,d),
inference(forward_demodulation,[],[f337,f26]) ).
fof(f350,plain,
additive_identity = b,
inference(forward_demodulation,[],[f346,f23]) ).
fof(f402,plain,
! [X0] :
( multiply(b,a) = X0
| ~ product(a,d,X0) ),
inference(forward_demodulation,[],[f135,f161]) ).
fof(f403,plain,
! [X0] :
( ~ product(a,d,X0)
| d = X0 ),
inference(forward_demodulation,[],[f402,f26]) ).
fof(f407,plain,
! [X0] : product(X0,d,d),
inference(superposition,[],[f32,f348]) ).
fof(f422,plain,
a = d,
inference(resolution,[],[f403,f94]) ).
fof(f452,plain,
a != b,
inference(superposition,[],[f182,f422]) ).
fof(f479,plain,
! [X0] : product(X0,a,a),
inference(forward_demodulation,[],[f407,f422]) ).
fof(f602,plain,
! [X0] :
( add(a,a) = X0
| ~ product(add(b,a),a,X0) ),
inference(forward_demodulation,[],[f127,f422]) ).
fof(f603,plain,
! [X0] :
( additive_identity = X0
| ~ product(add(b,a),a,X0) ),
inference(forward_demodulation,[],[f602,f23]) ).
fof(f604,plain,
! [X0] :
( ~ product(add(b,a),a,X0)
| b = X0 ),
inference(forward_demodulation,[],[f603,f350]) ).
fof(f629,plain,
a = b,
inference(resolution,[],[f604,f479]) ).
fof(f636,plain,
$false,
inference(forward_subsumption_resolution,[],[f629,f452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.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 22:59:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 3.63/1.47 % (1875029)Input is clausal, will run a generic CNF schedule.
% 3.63/1.47 % (1875040)dis-21_1_sil=8000:lcm=predicate:random_seed=1430834435: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)
% 3.63/1.47 % (1875040)Instruction limit reached!
% 3.63/1.47 % (1875040)------------------------------
% 3.63/1.47 % (1875040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.47 % (1875040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.47 % (1875040)CaDiCaL version: 2.1.3
% 3.63/1.47 % (1875040)Termination reason: Instruction limit
% 3.63/1.47 % (1875040)Termination phase: Saturation
% 3.63/1.47 % (1875040)Time elapsed: 0.038 s
% 3.63/1.47 % (1875040)Peak memory usage: 88 MB
% 3.63/1.47 % (1875040)Instructions burned: 120 (million)
% 3.63/1.47 % (1875037)lrs+10_1_sil=8000:sp=occurrence:random_seed=848694667:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.63/1.47 % (1875039)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=283163318:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.63/1.47 % (1875038)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2068825297:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.63/1.47 % (1875035)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=331179288:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.63/1.47 % (1875034)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=4044385617:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.63/1.47 % (1875036)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3593285584:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.63/1.47 % (1875039)First to succeed.
% 3.63/1.47 % (1875039)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1875029"
% 3.63/1.47 % (1875037)Also succeeded, but the first one will report.
% 3.63/1.47 % (1875038)Instruction limit reached!
% 3.63/1.47 % (1875038)------------------------------
% 3.63/1.47 % (1875038)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.47 % (1875038)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.47 % (1875038)CaDiCaL version: 2.1.3
% 3.63/1.47 % (1875038)Termination reason: Instruction limit
% 3.63/1.47 % (1875038)Termination phase: Saturation
% 3.63/1.47 % (1875038)Time elapsed: 0.068 s
% 3.63/1.47 % (1875038)Peak memory usage: 88 MB
% 3.63/1.47 % (1875038)Instructions burned: 114 (million)
% 3.63/1.47 % (1875042)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=758450086:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.63/1.47 % (1875042)Also succeeded, but the first one will report.
% 3.63/1.47 % (1875049)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2908060292: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)
% 3.63/1.47 % (1875039)Refutation found. Thanks to Tanya!
% 3.63/1.47 % SZS status Unsatisfiable for theBenchmark
% 3.63/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 3.63/1.47 % (1875039)------------------------------
% 3.63/1.47 % (1875039)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.47 % (1875039)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.47 % (1875039)CaDiCaL version: 2.1.3
% 3.63/1.47 % (1875039)Termination reason: Refutation
% 3.63/1.47 % (1875039)Time elapsed: 0.016 s
% 3.63/1.47 % (1875039)Peak memory usage: 88 MB
% 3.63/1.47 % (1875039)Instructions burned: 20 (million)
% 3.63/1.47 % (1875039)------------------------------
% 3.63/1.47 % (1875039)------------------------------
% 3.63/1.47 % (1875029)Success in time 0.434 s
% 3.63/1.47 % Vampire exiting
%------------------------------------------------------------------------------