%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG014-6 : 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 : 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 12:35:07 PM UTC 2026
% Result : Unsatisfiable 5.10s 1.81s
% Output : Refutation 5.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 28 unt; 2 def)
% Number of atoms : 47 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 8 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_identity) ).
fof(f2,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_identity) ).
fof(f5,axiom,
! [X0] : multiply(X0,additive_identity) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_multiplicative_zero) ).
fof(f6,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_additive_inverse) ).
fof(f8,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_additive_inverse) ).
fof(f10,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f9]) ).
fof(f12,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distribute1) ).
fof(f14,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_for_addition) ).
fof(f15,axiom,
! [X2,X0,X1] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_for_addition) ).
fof(f20,negated_conjecture,
multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f22,definition,
( spl0_1
<=> multiply(a,additive_inverse(b)) = additive_inverse(multiply(a,b)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f24,plain,
( multiply(a,additive_inverse(b)) != additive_inverse(multiply(a,b))
| spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f20,f22]) ).
fof(f28,plain,
additive_identity = additive_inverse(additive_identity),
inference(superposition,[],[f2,f8]) ).
fof(f30,definition,
( spl0_2
<=> additive_identity = additive_inverse(additive_identity) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f32,plain,
( additive_identity = additive_inverse(additive_identity)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f30]) ).
fof(f33,plain,
spl0_2,
inference(avatar_split_clause,[],[f28,f30]) ).
fof(f58,plain,
! [X0,X1] : add(additive_identity,X1) = add(additive_inverse(X0),add(X0,X1)),
inference(superposition,[],[f15,f8]) ).
fof(f67,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[],[f58,f1]) ).
fof(f87,plain,
! [X0,X1] : add(additive_inverse(X1),add(X0,X1)) = X0,
inference(superposition,[],[f67,f14]) ).
fof(f125,plain,
! [X0,X1] : additive_inverse(X1) = add(additive_inverse(add(X1,X0)),X0),
inference(superposition,[],[f87,f67]) ).
fof(f196,plain,
! [X0,X1] : additive_inverse(X0) = add(X1,additive_inverse(add(X0,X1))),
inference(superposition,[],[f14,f125]) ).
fof(f309,plain,
! [X0,X1] : multiply(X0,additive_identity) = add(multiply(X0,X1),multiply(X0,additive_inverse(X1))),
inference(superposition,[],[f12,f10]) ).
fof(f330,plain,
! [X0,X1] : additive_identity = add(multiply(X0,X1),multiply(X0,additive_inverse(X1))),
inference(forward_demodulation,[],[f309,f6]) ).
fof(f553,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = add(multiply(X0,additive_inverse(X1)),additive_inverse(additive_identity)),
inference(superposition,[],[f196,f330]) ).
fof(f556,plain,
( ! [X0,X1] : additive_inverse(multiply(X0,X1)) = add(multiply(X0,additive_inverse(X1)),additive_identity)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f553,f32]) ).
fof(f572,plain,
( ! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(X0,additive_inverse(X1))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f556,f2]) ).
fof(f579,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(backward_subsumption_resolution,[],[f24,f572]) ).
fof(f591,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f579]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f25]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f33]) ).
cnf(s4,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f591]) ).
cnf(s5,plain,
spl0_1,
inference(rat,[],[s4,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5]) ).
fof(f617,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : RNG014-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 23:04:47 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 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
% 5.10/1.81 % (4068530)Detected a unit-equality problem, will run specialized UEQ schedule.
% 5.10/1.81 % (4068535)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1592469791:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 5.10/1.81 % (4068540)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2143021826:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 5.10/1.81 % (4068540)First to succeed.
% 5.10/1.81 % (4068540)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4068530"
% 5.10/1.81 % (4068536)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2623164137:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 5.10/1.81 % (4068537)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1871133513:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 5.10/1.81 % (4068538)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3503451901:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 5.10/1.81 % (4068539)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3595490433:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 5.10/1.81 % (4068539)Refutation not found, incomplete strategy
% 5.10/1.81 % (4068539)------------------------------
% 5.10/1.81 % (4068539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.81 % (4068539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.81 % (4068539)CaDiCaL version: 2.1.3
% 5.10/1.81 % (4068539)Termination reason: Refutation not found, incomplete strategy
% 5.10/1.81 % (4068539)Time elapsed: 0.002 s
% 5.10/1.81 % (4068539)Peak memory usage: 87 MB
% 5.10/1.81 % (4068539)Instructions burned: 1 (million)
% 5.10/1.81 % (4068538)Also succeeded, but the first one will report.
% 5.10/1.81 % (4068541)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2098097791:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 5.10/1.81 % (4068541)Also succeeded, but the first one will report.
% 5.10/1.81 % (4068540)Refutation found. Thanks to Tanya!
% 5.10/1.81 % SZS status Unsatisfiable for theBenchmark
% 5.10/1.81 % SZS output start Proof for theBenchmark
% See solution above
% 5.10/1.81 % (4068540)------------------------------
% 5.10/1.81 % (4068540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.10/1.81 % (4068540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.10/1.81 % (4068540)CaDiCaL version: 2.1.3
% 5.10/1.81 % (4068540)Termination reason: Refutation
% 5.10/1.81 % (4068540)Time elapsed: 0.018 s
% 5.10/1.81 % (4068540)Peak memory usage: 89 MB
% 5.10/1.81 % (4068540)Instructions burned: 22 (million)
% 5.10/1.81 % (4068540)------------------------------
% 5.10/1.81 % (4068540)------------------------------
% 5.10/1.81 % (4068530)Success in time 0.608 s
% 5.10/1.81 % Vampire exiting
%------------------------------------------------------------------------------