%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI740_1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 09:33:46 AM UTC 2026
% Result : Theorem 2.77s 1.09s
% Output : Refutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 50 ( 25 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 15 ~; 13 |; 0 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 93 ( 7 atm; 16 fun; 54 num; 16 var)
% Number of types : 2 ( 0 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 2 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
power: ( $real * $int ) > $real ).
tff(func_def_12,type,
sF0: $real ).
tff(f2,axiom,
! [X1: $int,X0: $real] :
( $lesseq(0,X1)
=> ( power(X0,$sum(X1,1)) = $product(X0,power(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_s) ).
tff(f4,axiom,
! [X0: $real] : ( power(X0,1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_1) ).
tff(f9,conjecture,
power(2/1,2) = 4/1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pow_2_2) ).
tff(f10,negated_conjecture,
( ( ~ power(2/1,2) ) = 4/1 ),
inference(negated_conjecture,[status(cth)],[f9]) ).
tff(f15,plain,
! [X1: $int,X0: $real] :
( ~ $less(X1,0)
=> ( power(X0,$sum(X1,1)) = $product(X0,power(X0,X1)) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f19,plain,
power(2/1,2) != 4/1,
inference(flattening,[],[f10]) ).
tff(f20,plain,
! [X0: $int,X1: $real] :
( ~ $less(X0,0)
=> ( power(X1,$sum(X0,1)) = $product(X1,power(X1,X0)) ) ),
inference(rectify,[],[f15]) ).
tff(f27,plain,
! [X1: $real,X0: $int] :
( ( power(X1,$sum(X0,1)) = $product(X1,power(X1,X0)) )
| $less(X0,0) ),
inference(ennf_transformation,[],[f20]) ).
tff(f32,plain,
! [X0: $real,X1: $int] :
( ( power(X0,$sum(X1,1)) = $product(X0,power(X0,X1)) )
| $less(X1,0) ),
inference(rectify,[],[f27]) ).
tff(f39,plain,
! [X0: $real,X1: $int] :
( ( power(X0,$sum(X1,1)) = $product(X0,power(X0,X1)) )
| $less(X1,0) ),
inference(cnf_transformation,[],[f32]) ).
tff(f40,plain,
power(2/1,2) != 4/1,
inference(cnf_transformation,[],[f19]) ).
tff(f42,plain,
! [X0: $real] : ( power(X0,1) = X0 ),
inference(cnf_transformation,[],[f4]) ).
tff(f45,definition,
sF0 = power(2/1,2),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
tff(f46,plain,
power(2/1,2) = sF0,
inference(reorient_equations,[],[f45]) ).
tff(f47,plain,
4/1 != sF0,
inference(definition_folding,[],[f40,f46]) ).
tff(f50,definition,
( spl1_1
<=> ( power(2/1,2) = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f52,plain,
( ( power(2/1,2) = sF0 )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f50]) ).
tff(f53,plain,
spl1_1,
inference(avatar_split_clause,[],[f46,f50]) ).
tff(f55,definition,
( spl1_2
<=> ( 4/1 = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f57,plain,
( ( 4/1 != sF0 )
| spl1_2 ),
inference(avatar_component_clause,[],[f55]) ).
tff(f58,plain,
~ spl1_2,
inference(avatar_split_clause,[],[f47,f55]) ).
tff(f59,plain,
( ( power(2/1,2) != 4/1 )
| ~ spl1_1
| spl1_2 ),
inference(superposition,[],[f57,f52]) ).
tff(f61,definition,
( spl1_3
<=> ( power(2/1,2) = 4/1 ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f63,plain,
( ( power(2/1,2) != 4/1 )
| spl1_3 ),
inference(avatar_component_clause,[],[f61]) ).
tff(f64,plain,
( ~ spl1_3
| ~ spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f59,f55,f50,f61]) ).
tff(f68,plain,
! [X0: $real] :
( $less(1,0)
| ( $product(X0,X0) = power(X0,$sum(1,1)) ) ),
inference(superposition,[],[f39,f42]) ).
tff(f71,plain,
! [X0: $real] : ( $product(X0,X0) = power(X0,2) ),
inference(evaluation,[],[f68]) ).
tff(f77,plain,
( ( 4/1 != $product(2/1,2/1) )
| spl1_3 ),
inference(superposition,[],[f63,f71]) ).
tff(f79,plain,
( $false
| spl1_3 ),
inference(evaluation,[],[f77]) ).
tff(f80,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f79]) ).
tff(f82,plain,
$false,
inference(avatar_smt_refutation,[],[f80,f64,f58,f53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI740_1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:02:49 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.77/1.09 % (553196)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.77/1.09 % (553309)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1637630587:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.77/1.09 % (553309)First to succeed.
% 2.77/1.09 % (553309)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-553196"
% 2.77/1.09 % (553313)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3345648093:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.77/1.09 % (553318)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=4279035333:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.77/1.09 % (553316)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1678409112:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.77/1.09 % (553311)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1896383512:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.77/1.09 % (553314)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3579016784:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.77/1.09 % (553308)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=302402154:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.77/1.09 % (553314)Instruction limit reached!
% 2.77/1.09 % (553314)------------------------------
% 2.77/1.09 % (553314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.09 % (553314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.09 % (553314)CaDiCaL version: 2.1.3
% 2.77/1.09 % (553314)Termination reason: Instruction limit
% 2.77/1.09 % (553314)Termination phase: Saturation
% 2.77/1.09 % (553314)Time elapsed: 0.004 s
% 2.77/1.09 % (553314)Peak memory usage: 88 MB
% 2.77/1.09 % (553314)Instructions burned: 5 (million)
% 2.77/1.09 % (553313)Instruction limit reached!
% 2.77/1.09 % (553313)------------------------------
% 2.77/1.09 % (553313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.09 % (553313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.09 % (553313)CaDiCaL version: 2.1.3
% 2.77/1.09 % (553313)Termination reason: Instruction limit
% 2.77/1.09 % (553313)Termination phase: Saturation
% 2.77/1.09 % (553313)Time elapsed: 0.005 s
% 2.77/1.09 % (553313)Peak memory usage: 88 MB
% 2.77/1.09 % (553313)Instructions burned: 7 (million)
% 2.77/1.09 % (553316)Refutation not found, incomplete strategy
% 2.77/1.09 % (553316)------------------------------
% 2.77/1.09 % (553316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.09 % (553316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.09 % (553316)CaDiCaL version: 2.1.3
% 2.77/1.09 % (553316)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.09 % (553316)Time elapsed: 0.031 s
% 2.77/1.09 % (553316)Peak memory usage: 115 MB
% 2.77/1.09 % (553316)Instructions burned: 8 (million)
% 2.77/1.09 % (553308)Refutation not found, incomplete strategy
% 2.77/1.09 % (553308)------------------------------
% 2.77/1.09 % (553308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.09 % (553308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.09 % (553308)CaDiCaL version: 2.1.3
% 2.77/1.09 % (553308)Termination reason: Refutation not found, incomplete strategy
% 2.77/1.09 % (553308)Time elapsed: 0.032 s
% 2.77/1.09 % (553308)Peak memory usage: 116 MB
% 2.77/1.09 % (553308)Instructions burned: 10 (million)
% 2.77/1.09 % (553318)Instruction limit reached!
% 2.77/1.09 % (553318)------------------------------
% 2.77/1.09 % (553318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.09 % (553318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.09 % (553318)CaDiCaL version: 2.1.3
% 2.77/1.09 % (553318)Termination reason: Instruction limit
% 2.77/1.09 % (553318)Termination phase: Saturation
% 2.77/1.09 % (553318)Time elapsed: 0.046 s
% 2.77/1.09 % (553318)Peak memory usage: 115 MB
% 2.77/1.09 % (553318)Instructions burned: 34 (million)
% 2.77/1.09 % (553309)Refutation found. Thanks to Tanya!
% 2.77/1.09 % SZS status Theorem for theBenchmark
% 2.77/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 2.77/1.09 % (553309)------------------------------
% 2.77/1.09 % (553309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.77/1.09 % (553309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.77/1.09 % (553309)CaDiCaL version: 2.1.3
% 2.77/1.09 % (553309)Termination reason: Refutation
% 2.77/1.09 % (553309)Time elapsed: 0.021 s
% 2.77/1.09 % (553309)Peak memory usage: 116 MB
% 2.77/1.09 % (553309)Instructions burned: 11 (million)
% 2.77/1.09 % (553309)------------------------------
% 2.77/1.09 % (553309)------------------------------
% 2.77/1.09 % (553196)Success in time 0.312 s
% 2.77/1.09 % Vampire exiting
%------------------------------------------------------------------------------