%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG008-3 : 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 : n026.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 12:35:06 PM UTC 2026
% Result : Unsatisfiable 0.17s 1.40s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 52 ( 43 unt; 2 def)
% Number of atoms : 63 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 12 ~; 9 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : add(additive_identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute1) ).
fof(f5,axiom,
! [X2,X0,X1] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distribute2) ).
fof(f8,axiom,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse_additive_inverse) ).
fof(f14,axiom,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse1) ).
fof(f15,axiom,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_additive_inverse2) ).
fof(f16,plain,
! [X0,X1] : additive_inverse(multiply(X0,X1)) = multiply(additive_inverse(X0),X1),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associative_addition) ).
fof(f18,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutative_addition) ).
fof(f20,axiom,
! [X0] : add(X0,additive_identity) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f21,axiom,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f22,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(reorient_equations,[],[f21]) ).
fof(f23,axiom,
! [X0] : multiply(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolean_ring) ).
fof(f24,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f25,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_commutativity) ).
fof(f26,plain,
c != multiply(b,a),
inference(reorient_equations,[],[f25]) ).
fof(f28,definition,
( spl0_1
<=> c = multiply(b,a) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f30,plain,
( c != multiply(b,a)
| spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f26,f28]) ).
fof(f33,definition,
( spl0_2
<=> multiply(a,b) = c ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f35,plain,
( multiply(a,b) = c
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
spl0_2,
inference(avatar_split_clause,[],[f24,f33]) ).
fof(f67,plain,
! [X0] : additive_inverse(X0) = additive_inverse(multiply(additive_inverse(X0),X0)),
inference(superposition,[],[f23,f14]) ).
fof(f70,plain,
! [X0] : additive_inverse(X0) = additive_inverse(additive_inverse(multiply(X0,X0))),
inference(forward_demodulation,[],[f67,f16]) ).
fof(f75,plain,
! [X0] : additive_inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[],[f70,f8]) ).
fof(f77,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[],[f75,f23]) ).
fof(f84,plain,
! [X0] : additive_identity = add(X0,X0),
inference(backward_demodulation,[],[f22,f77]) ).
fof(f90,plain,
! [X0,X1] : add(additive_identity,X1) = add(X0,add(X0,X1)),
inference(superposition,[],[f17,f84]) ).
fof(f101,plain,
! [X0,X1] : add(X0,add(X0,X1)) = X1,
inference(forward_demodulation,[],[f90,f1]) ).
fof(f123,plain,
! [X0,X1] : add(X1,add(X0,X1)) = X0,
inference(superposition,[],[f101,f18]) ).
fof(f190,plain,
! [X0,X1] : add(X0,X1) = add(multiply(add(X0,X1),X0),multiply(add(X0,X1),X1)),
inference(superposition,[],[f23,f4]) ).
fof(f199,plain,
! [X0,X1] : add(X0,X1) = add(multiply(add(X0,X1),X0),add(multiply(X0,X1),multiply(X1,X1))),
inference(forward_demodulation,[],[f190,f5]) ).
fof(f215,plain,
! [X0,X1] : add(X0,X1) = add(multiply(add(X0,X1),X0),add(multiply(X0,X1),X1)),
inference(forward_demodulation,[],[f199,f23]) ).
fof(f222,plain,
! [X0,X1] : add(X0,X1) = add(add(multiply(X0,X0),multiply(X1,X0)),add(multiply(X0,X1),X1)),
inference(forward_demodulation,[],[f215,f5]) ).
fof(f227,plain,
! [X0,X1] : add(X0,X1) = add(multiply(X0,X0),add(multiply(X1,X0),add(multiply(X0,X1),X1))),
inference(forward_demodulation,[],[f222,f17]) ).
fof(f229,plain,
! [X0,X1] : add(X0,X1) = add(X0,add(multiply(X1,X0),add(multiply(X0,X1),X1))),
inference(forward_demodulation,[],[f227,f23]) ).
fof(f1182,plain,
! [X0,X1] : add(X0,add(X0,X1)) = add(multiply(X1,X0),add(multiply(X0,X1),X1)),
inference(superposition,[],[f101,f229]) ).
fof(f1197,plain,
! [X0,X1] : add(multiply(X1,X0),add(multiply(X0,X1),X1)) = X1,
inference(forward_demodulation,[],[f1182,f101]) ).
fof(f1419,plain,
! [X0,X1] : multiply(X0,X1) = add(add(multiply(X1,X0),X0),X0),
inference(superposition,[],[f123,f1197]) ).
fof(f1430,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(X1,X0),add(X0,X0)),
inference(forward_demodulation,[],[f1419,f17]) ).
fof(f1479,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(X1,X0),additive_identity),
inference(forward_demodulation,[],[f1430,f84]) ).
fof(f1510,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[],[f1479,f20]) ).
fof(f1601,plain,
( multiply(a,b) != c
| spl0_1 ),
inference(superposition,[],[f30,f1510]) ).
fof(f1621,plain,
( c != c
| spl0_1
| ~ spl0_2 ),
inference(forward_demodulation,[],[f1601,f35]) ).
fof(f1622,plain,
( $false
| spl0_1
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f1621]) ).
fof(f1623,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f1622]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f31]) ).
cnf(s2,plain,
spl0_2,
inference(sat_conversion,[],[f36]) ).
cnf(s18,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f1623]) ).
cnf(s19,plain,
spl0_1,
inference(rat,[],[s18,s2]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s1,s19]) ).
fof(f1632,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n026.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 23:01:27 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.42 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
% 0.17/1.40 % (3311312)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.17/1.40 % (3311319)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2323559938:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.17/1.40 % (3311320)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=992271300:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.17/1.40 % (3311318)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=2959177443:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.17/1.40 % (3311317)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=1431217260:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.17/1.40 % (3311321)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1126723300:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.17/1.40 % (3311323)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=79684910:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.17/1.40 % (3311322)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1671132344:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.17/1.40 % (3311322)First to succeed.
% 0.17/1.40 % (3311322)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3311312"
% 0.17/1.40 % (3311323)Also succeeded, but the first one will report.
% 0.17/1.40 % (3311320)Also succeeded, but the first one will report.
% 0.17/1.40 % (3311321)Also succeeded, but the first one will report.
% 0.17/1.40 % (3311322)Refutation found. Thanks to Tanya!
% 0.17/1.40 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.40 % (3311322)------------------------------
% 0.17/1.40 % (3311322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.40 % (3311322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.40 % (3311322)CaDiCaL version: 2.1.3
% 0.17/1.40 % (3311322)Termination reason: Refutation
% 0.17/1.40 % (3311322)Time elapsed: 0.033 s
% 0.17/1.40 % (3311322)Peak memory usage: 89 MB
% 0.17/1.40 % (3311322)Instructions burned: 50 (million)
% 0.17/1.40 % (3311322)------------------------------
% 0.17/1.40 % (3311322)------------------------------
% 0.17/1.40 % (3311312)Success in time 0.452 s
% 0.17/1.40 % Vampire exiting
%------------------------------------------------------------------------------