%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM907_1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:17:24 PM UTC 2026
% Result : Theorem 3.13s 1.41s
% Output : Refutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 13 unt; 0 typ; 3 def)
% Number of atoms : 125 ( 72 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 49 ~; 48 |; 13 &)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 185 ( 0 atm; 140 fun; 5 num; 40 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 28 !; 12 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_5,type,
sK0: $rat ).
tff(func_def_6,type,
sK1: $rat ).
tff(func_def_7,type,
sK2: $rat ).
tff(func_def_10,type,
'$inst4': $rat ).
tff(f1,conjecture,
! [X1: $rat,X2: $rat,X0: $rat] :
( ( $sum(X0,X1) = X2 )
<=> ( ( $difference(X2,X0) = X1 )
& ( $difference(X2,X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rat_combined_problem_2) ).
tff(f2,negated_conjecture,
~ ! [X1: $rat,X2: $rat,X0: $rat] :
( ( $sum(X0,X1) = X2 )
<=> ( ( $difference(X2,X0) = X1 )
& ( $difference(X2,X1) = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $rat,X2: $rat,X0: $rat] :
( ( $sum(X0,X1) = X2 )
<=> ( ( $sum(X2,$uminus(X0)) = X1 )
& ( $sum(X2,$uminus(X1)) = X0 ) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f5,plain,
! [X2: $rat,X0: $rat,X1: $rat] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(definition,[],[tha_associativity]) ).
tff(f7,plain,
! [X0: $rat,X1: $rat] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(definition,[],[tha_inverse_op_op_inverses]) ).
tff(f8,plain,
! [X0: $rat] : ( $sum(X0,$uminus(X0)) = 0/1 ),
introduced(definition,[],[tha_inverse_op_unit]) ).
tff(f14,plain,
! [X0: $rat] : ( $uminus($uminus(X0)) = X0 ),
introduced(definition,[],[tha_minus_minus_x]) ).
tff(f15,plain,
~ ! [X1: $rat,X0: $rat,X2: $rat] :
( ( $sum(X2,X0) = X1 )
<=> ( ( $sum(X1,$uminus(X0)) = X2 )
& ( $sum(X1,$uminus(X2)) = X0 ) ) ),
inference(rectify,[],[f3]) ).
tff(f16,plain,
? [X1: $rat,X2: $rat,X0: $rat] :
( ( ( $sum(X1,$uminus(X0)) = X2 )
& ( $sum(X1,$uminus(X2)) = X0 ) )
<~> ( $sum(X2,X0) = X1 ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f17,plain,
? [X1: $rat,X2: $rat,X0: $rat] :
( ( ( $sum(X2,X0) != X1 )
| ( $sum(X1,$uminus(X0)) != X2 )
| ( $sum(X1,$uminus(X2)) != X0 ) )
& ( ( $sum(X2,X0) = X1 )
| ( ( $sum(X1,$uminus(X0)) = X2 )
& ( $sum(X1,$uminus(X2)) = X0 ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
tff(f18,plain,
? [X1: $rat,X2: $rat,X0: $rat] :
( ( ( $sum(X2,X0) != X1 )
| ( $sum(X1,$uminus(X0)) != X2 )
| ( $sum(X1,$uminus(X2)) != X0 ) )
& ( ( $sum(X2,X0) = X1 )
| ( ( $sum(X1,$uminus(X0)) = X2 )
& ( $sum(X1,$uminus(X2)) = X0 ) ) ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
? [X0: $rat,X1: $rat,X2: $rat] :
( ( ( $sum(X1,X2) != X0 )
| ( $sum(X0,$uminus(X2)) != X1 )
| ( $sum(X0,$uminus(X1)) != X2 ) )
& ( ( $sum(X1,X2) = X0 )
| ( ( $sum(X0,$uminus(X2)) = X1 )
& ( $sum(X0,$uminus(X1)) = X2 ) ) ) ),
inference(rectify,[],[f18]) ).
tff(f20,plain,
( ( ( sK0 != $sum(sK1,sK2) )
| ( $sum(sK0,$uminus(sK2)) != sK1 )
| ( sK2 != $sum(sK0,$uminus(sK1)) ) )
& ( ( sK0 = $sum(sK1,sK2) )
| ( ( $sum(sK0,$uminus(sK2)) = sK1 )
& ( sK2 = $sum(sK0,$uminus(sK1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
tff(f22,plain,
( ( sK0 = $sum(sK1,sK2) )
| ( $sum(sK0,$uminus(sK2)) = sK1 ) ),
inference(cnf_transformation,[],[f20]) ).
tff(f23,plain,
( ( sK2 != $sum(sK0,$uminus(sK1)) )
| ( $sum(sK0,$uminus(sK2)) != sK1 )
| ( sK0 != $sum(sK1,sK2) ) ),
inference(cnf_transformation,[],[f20]) ).
tff(f25,definition,
( spl3_1
<=> ( sK0 = $sum(sK1,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f26,plain,
( ( sK0 != $sum(sK1,sK2) )
| spl3_1 ),
inference(avatar_component_clause,[],[f25]) ).
tff(f27,plain,
( ( sK0 = $sum(sK1,sK2) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f25]) ).
tff(f29,definition,
( spl3_2
<=> ( sK2 = $sum(sK0,$uminus(sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f34,definition,
( spl3_3
<=> ( $sum(sK0,$uminus(sK2)) = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f35,plain,
( ( $sum(sK0,$uminus(sK2)) != sK1 )
| spl3_3 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f36,plain,
( ( $sum(sK0,$uminus(sK2)) = sK1 )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f34]) ).
tff(f37,plain,
( spl3_1
| spl3_3 ),
inference(avatar_split_clause,[],[f22,f34,f25]) ).
tff(f38,plain,
( ~ spl3_3
| ~ spl3_2
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f23,f25,f29,f34]) ).
tff(f39,plain,
! [X0: $rat] : ( $sum($uminus(X0),X0) = 0/1 ),
inference(superposition,[],[f8,f14]) ).
tff(f173,plain,
( ! [X0: $rat] : ( $sum(sK1,X0) = $sum(sK0,$sum($uminus(sK2),X0)) )
| ~ spl3_3 ),
inference(superposition,[],[f5,f36]) ).
tff(f174,plain,
! [X0: $rat,X1: $rat] : ( $sum(0/1,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f5,f8]) ).
tff(f193,plain,
! [X0: $rat,X1: $rat] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f174]) ).
tff(f244,plain,
( ( $sum(sK0,0/1) = $sum(sK1,sK2) )
| ~ spl3_3 ),
inference(superposition,[],[f173,f39]) ).
tff(f255,plain,
( ( sK0 = $sum(sK1,sK2) )
| ~ spl3_3 ),
inference(evaluation,[],[f244]) ).
tff(f260,plain,
( $false
| spl3_1
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f255,f26]) ).
tff(f261,plain,
( spl3_1
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f260]) ).
tff(f268,plain,
( ( sK0 = $sum(sK2,sK1) )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f27,f4]) ).
tff(f269,plain,
( ! [X0: $rat] : ( $sum(sK0,X0) = $sum(sK2,$sum(sK1,X0)) )
| ~ spl3_1 ),
inference(superposition,[],[f5,f268]) ).
tff(f272,plain,
( ( $uminus(sK0) = $sum($uminus(sK1),$uminus(sK2)) )
| ~ spl3_1 ),
inference(superposition,[],[f7,f268]) ).
tff(f273,plain,
( ( $uminus(sK0) = $sum($uminus(sK2),$uminus(sK1)) )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f272,f4]) ).
tff(f432,plain,
( ( $sum(sK0,$uminus(sK1)) = $sum(sK2,0/1) )
| ~ spl3_1 ),
inference(superposition,[],[f269,f8]) ).
tff(f439,plain,
( ( sK2 = $sum(sK0,$uminus(sK1)) )
| ~ spl3_1 ),
inference(evaluation,[],[f432]) ).
tff(f447,plain,
( spl3_2
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f439,f25,f29]) ).
tff(f589,plain,
( ( $uminus(sK1) = $sum(sK2,$uminus(sK0)) )
| ~ spl3_1 ),
inference(superposition,[],[f193,f273]) ).
tff(f1785,plain,
( ( $uminus($sum(sK2,$uminus(sK0))) = sK1 )
| ~ spl3_1 ),
inference(superposition,[],[f14,f589]) ).
tff(f1786,plain,
( ( sK1 = $sum($uminus($uminus(sK0)),$uminus(sK2)) )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f1785,f7]) ).
tff(f1787,plain,
( ( $sum(sK0,$uminus(sK2)) = sK1 )
| ~ spl3_1 ),
inference(evaluation,[],[f1786]) ).
tff(f1791,plain,
( $false
| ~ spl3_1
| spl3_3 ),
inference(forward_subsumption_resolution,[],[f1787,f35]) ).
tff(f1792,plain,
( ~ spl3_1
| spl3_3 ),
inference(avatar_contradiction_clause,[],[f1791]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f37]) ).
cnf(s3,plain,
( ~ spl3_1
| ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s12,plain,
( spl3_1
| ~ spl3_3 ),
inference(sat_conversion,[],[f261]) ).
cnf(s21,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f447]) ).
cnf(s26,plain,
( ~ spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f1792]) ).
cnf(s27,plain,
spl3_1,
inference(rat,[],[s2,s12]) ).
cnf(s28,plain,
spl3_3,
inference(rat,[],[s26,s27]) ).
cnf(s29,plain,
spl3_2,
inference(rat,[],[s21,s27]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s3,s28,s29,s27]) ).
tff(f1793,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM907_1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n007.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 21:37:10 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 3.13/1.41 % (1801542)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.13/1.41 % (1801549)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1324662087:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.13/1.41 % (1801553)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2615084905:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.13/1.41 % (1801550)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2911228125:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.13/1.41 % (1801551)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=824916984:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.13/1.41 % (1801548)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=529705157:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.13/1.41 % (1801547)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4147440229:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.13/1.41 % (1801552)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2060874421:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.13/1.41 % (1801551)Instruction limit reached!
% 3.13/1.41 % (1801551)------------------------------
% 3.13/1.41 % (1801551)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.41 % (1801551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.41 % (1801551)CaDiCaL version: 2.1.3
% 3.13/1.41 % (1801551)Termination reason: Instruction limit
% 3.13/1.41 % (1801551)Termination phase: Saturation
% 3.13/1.41 % (1801551)Time elapsed: 0.004 s
% 3.13/1.41 % (1801551)Peak memory usage: 88 MB
% 3.13/1.41 % (1801551)Instructions burned: 5 (million)
% 3.13/1.41 % (1801550)Instruction limit reached!
% 3.13/1.41 % (1801550)------------------------------
% 3.13/1.41 % (1801550)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.41 % (1801550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.41 % (1801550)CaDiCaL version: 2.1.3
% 3.13/1.41 % (1801550)Termination reason: Instruction limit
% 3.13/1.41 % (1801550)Termination phase: Saturation
% 3.13/1.41 % (1801550)Time elapsed: 0.005 s
% 3.13/1.41 % (1801550)Peak memory usage: 88 MB
% 3.13/1.41 % (1801550)Instructions burned: 7 (million)
% 3.13/1.41 % (1801549)First to succeed.
% 3.13/1.41 % (1801549)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1801542"
% 3.13/1.41 % (1801552)Also succeeded, but the first one will report.
% 3.13/1.41 % (1801547)Also succeeded, but the first one will report.
% 3.13/1.41 % (1801548)Also succeeded, but the first one will report.
% 3.13/1.41 % (1801553)Also succeeded, but the first one will report.
% 3.13/1.41 % (1801549)Refutation found. Thanks to Tanya!
% 3.13/1.41 % SZS status Theorem for theBenchmark
% 3.13/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 3.13/1.41 % (1801549)------------------------------
% 3.13/1.41 % (1801549)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.41 % (1801549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.41 % (1801549)CaDiCaL version: 2.1.3
% 3.13/1.41 % (1801549)Termination reason: Refutation
% 3.13/1.41 % (1801549)Time elapsed: 0.056 s
% 3.13/1.41 % (1801549)Peak memory usage: 118 MB
% 3.13/1.41 % (1801549)Instructions burned: 98 (million)
% 3.13/1.41 % (1801549)------------------------------
% 3.13/1.41 % (1801549)------------------------------
% 3.13/1.41 % (1801542)Success in time 0.352 s
% 3.13/1.41 % Vampire exiting
%------------------------------------------------------------------------------