%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI186_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 09:32:39 AM UTC 2026
% Result : Theorem 0.20s 1.20s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 29 ( 14 ~; 5 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 108 ( 0 atm; 12 fun; 80 num; 16 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 : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
g: ( $int * $int ) > $int ).
tff(func_def_11,type,
-1: $int > $int ).
tff(func_def_12,type,
-2: $int > $int ).
tff(func_def_13,type,
2: $int > $int ).
tff(func_def_14,type,
3: $int > $int ).
tff(f1,conjecture,
( ! [X1: $int,X0: $int] : ( g(X0,X1) = g(X0,$sum(X1,2)) )
=> ( ( g(3,3) = g(3,4) )
=> ( g(3,2) = g(3,5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X1: $int,X0: $int] : ( g(X0,X1) = g(X0,$sum(X1,2)) )
=> ( ( g(3,3) = g(3,4) )
=> ( g(3,2) = g(3,5) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f15,plain,
( ( g(3,2) != g(3,5) )
& ( g(3,3) = g(3,4) )
& ! [X1: $int,X0: $int] : ( g(X0,X1) = g(X0,$sum(X1,2)) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
( ! [X1: $int,X0: $int] : ( g(X0,X1) = g(X0,$sum(X1,2)) )
& ( g(3,3) = g(3,4) )
& ( g(3,2) != g(3,5) ) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
( ! [X0: $int,X1: $int] : ( g(X1,$sum(X0,2)) = g(X1,X0) )
& ( g(3,3) = g(3,4) )
& ( g(3,2) != g(3,5) ) ),
inference(rectify,[],[f16]) ).
tff(f18,plain,
g(3,2) != g(3,5),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
g(3,3) = g(3,4),
inference(cnf_transformation,[],[f17]) ).
tff(f20,plain,
! [X0: $int,X1: $int] : ( g(X1,$sum(X0,2)) = g(X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
tff(f23,plain,
! [X0: $int] :
( ( g(3,3) = g(3,X0) )
| ( 4 != $sum(X0,2) ) ),
inference(constrained_superposition,[],[f20,f19]) ).
tff(f25,plain,
! [X0: $int] :
( ( g(3,2) != g(3,X0) )
| ( 5 != $sum(X0,2) ) ),
inference(constrained_superposition,[],[f18,f20]) ).
tff(f34,plain,
! [X0: $int] :
( ( 5 != $sum(3,2) )
| ( g(3,2) != g(3,X0) )
| ( 4 != $sum(X0,2) ) ),
inference(constrained_superposition,[],[f25,f23]) ).
tff(f38,plain,
! [X0: $int] :
( ( g(3,2) != g(3,X0) )
| ( 4 != $sum(X0,2) ) ),
inference(evaluation,[],[f34]) ).
tff(f52,plain,
4 != $sum(2,2),
inference(equality_resolution,[],[f38]) ).
tff(f54,plain,
$false,
inference(evaluation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI186_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:44:30 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 0.20/1.20 % (3441233)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 0.20/1.20 % (3441245)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2979564464:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/1.20 % (3441245)Instruction limit reached!
% 0.20/1.20 % (3441245)------------------------------
% 0.20/1.20 % (3441245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441245)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441245)Termination reason: Instruction limit
% 0.20/1.20 % (3441245)Termination phase: Saturation
% 0.20/1.20 % (3441245)Time elapsed: 0.003 s
% 0.20/1.20 % (3441245)Peak memory usage: 88 MB
% 0.20/1.20 % (3441245)Instructions burned: 8 (million)
% 0.20/1.20 % (3441247)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3289182060:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 0.20/1.20 % (3441242)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3208371565:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/1.20 % (3441246)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1921870585:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 0.20/1.20 % (3441244)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2454728066:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 0.20/1.20 % (3441243)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1930972543:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 0.20/1.20 % (3441248)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1475542545:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 0.20/1.20 % (3441246)First to succeed.
% 0.20/1.20 % (3441246)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3441233"
% 0.20/1.20 % (3441247)Refutation not found, incomplete strategy
% 0.20/1.20 % (3441247)------------------------------
% 0.20/1.20 % (3441247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441247)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441247)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.20 % (3441247)Time elapsed: 0.029 s
% 0.20/1.20 % (3441247)Peak memory usage: 114 MB
% 0.20/1.20 % (3441247)Instructions burned: 6 (million)
% 0.20/1.20 % (3441242)Refutation not found, incomplete strategy
% 0.20/1.20 % (3441242)------------------------------
% 0.20/1.20 % (3441242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441242)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441242)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.20 % (3441242)Time elapsed: 0.029 s
% 0.20/1.20 % (3441242)Peak memory usage: 115 MB
% 0.20/1.20 % (3441242)Instructions burned: 6 (million)
% 0.20/1.20 % (3441243)Refutation not found, incomplete strategy
% 0.20/1.20 % (3441243)------------------------------
% 0.20/1.20 % (3441243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441243)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441243)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.20 % (3441243)Time elapsed: 0.030 s
% 0.20/1.20 % (3441243)Peak memory usage: 115 MB
% 0.20/1.20 % (3441243)Instructions burned: 9 (million)
% 0.20/1.20 % (3441248)Instruction limit reached!
% 0.20/1.20 % (3441248)------------------------------
% 0.20/1.20 % (3441248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441248)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441248)Termination reason: Instruction limit
% 0.20/1.20 % (3441248)Termination phase: Saturation
% 0.20/1.20 % (3441248)Time elapsed: 0.044 s
% 0.20/1.20 % (3441248)Peak memory usage: 115 MB
% 0.20/1.20 % (3441248)Instructions burned: 33 (million)
% 0.20/1.20 % (3441250)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=242632026:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.20/1.20 % (3441250)Refutation not found, incomplete strategy
% 0.20/1.20 % (3441250)------------------------------
% 0.20/1.20 % (3441250)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441250)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441250)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441250)Termination reason: Refutation not found, incomplete strategy
% 0.20/1.20 % (3441250)Time elapsed: 0.001 s
% 0.20/1.20 % (3441250)Peak memory usage: 89 MB
% 0.20/1.20 % (3441244)Instruction limit reached!
% 0.20/1.20 % (3441244)------------------------------
% 0.20/1.20 % (3441244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441244)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441244)Termination reason: Instruction limit
% 0.20/1.20 % (3441244)Termination phase: Saturation
% 0.20/1.20 % (3441244)Time elapsed: 0.154 s
% 0.20/1.20 % (3441244)Peak memory usage: 114 MB
% 0.20/1.20 % (3441244)Instructions burned: 201 (million)
% 0.20/1.20 % (3441257)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=629360820:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 0.20/1.20 % (3441257)Instruction limit reached!
% 0.20/1.20 % (3441257)------------------------------
% 0.20/1.20 % (3441257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441257)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441257)Termination reason: Instruction limit
% 0.20/1.20 % (3441257)Termination phase: Saturation
% 0.20/1.20 % (3441257)Time elapsed: 0.016 s
% 0.20/1.20 % (3441257)Peak memory usage: 88 MB
% 0.20/1.20 % (3441257)Instructions burned: 30 (million)
% 0.20/1.20 % (3441250)------------------------------
% 0.20/1.20 % (3441250)------------------------------
% 0.20/1.20 % (3441246)Refutation found. Thanks to Tanya!
% 0.20/1.20 % SZS status Theorem for theBenchmark
% 0.20/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.20 % (3441246)------------------------------
% 0.20/1.20 % (3441246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (3441246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (3441246)CaDiCaL version: 2.1.3
% 0.20/1.20 % (3441246)Termination reason: Refutation
% 0.20/1.20 % (3441246)Time elapsed: 0.003 s
% 0.20/1.20 % (3441246)Peak memory usage: 89 MB
% 0.20/1.20 % (3441246)Instructions burned: 3 (million)
% 0.20/1.20 % (3441246)------------------------------
% 0.20/1.20 % (3441246)------------------------------
% 0.20/1.20 % (3441233)Success in time 0.434 s
% 0.20/1.20 % Vampire exiting
%------------------------------------------------------------------------------