%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI741_1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 5.55s 1.67s
% Output : Refutation 5.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 4 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 40 ( 5 atm; 4 fun; 25 num; 6 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 : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 6 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
exp: $real > $real ).
tff(func_def_5,type,
log: $real > $real ).
tff(func_def_6,type,
log2: $real > $real ).
tff(func_def_9,type,
log10: $real > $real ).
tff(func_def_11,type,
pow: ( $real * $real ) > $real ).
tff(func_def_12,type,
sqr: $real > $real ).
tff(func_def_13,type,
sqrt: $real > $real ).
tff(f16,axiom,
! [X0: $real] : ( sqr(X0) = $product(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sqr_def) ).
tff(f22,axiom,
! [X0: $real] :
( $less(0/1,X0)
=> ( pow(X0,2/1) = sqr(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pow_x_two) ).
tff(f24,conjecture,
pow(2/1,2/1) = 4/1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pow_2_21) ).
tff(f25,negated_conjecture,
( ( ~ pow(2/1,2/1) ) = 4/1 ),
inference(negated_conjecture,[status(cth)],[f24]) ).
tff(f52,plain,
pow(2/1,2/1) != 4/1,
inference(flattening,[],[f25]) ).
tff(f68,plain,
! [X0: $real] :
( ( pow(X0,2/1) = sqr(X0) )
| ~ $less(0/1,X0) ),
inference(ennf_transformation,[],[f22]) ).
tff(f86,plain,
! [X0: $real] : ( sqr(X0) = $product(X0,X0) ),
inference(cnf_transformation,[],[f16]) ).
tff(f89,plain,
! [X0: $real] :
( ( sqr(X0) = pow(X0,2/1) )
| ~ $less(0/1,X0) ),
inference(cnf_transformation,[],[f68]) ).
tff(f91,plain,
pow(2/1,2/1) != 4/1,
inference(cnf_transformation,[],[f52]) ).
tff(f103,plain,
! [X0: $real] :
( ( $product(X0,X0) = pow(X0,2/1) )
| ~ $less(0/1,X0) ),
inference(definition_unfolding,[],[f89,f86]) ).
tff(f146,plain,
( ( 4/1 != $product(2/1,2/1) )
| ~ $less(0/1,2/1) ),
inference(superposition,[],[f91,f103]) ).
tff(f161,plain,
$false,
inference(evaluation,[],[f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI741_1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 21:01:52 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running first-order theorem proving
% 0.24/0.28 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
% 5.55/1.67 % (771315)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.55/1.67 % (771324)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1753146121:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.55/1.67 % (771324)Instruction limit reached!
% 5.55/1.67 % (771324)------------------------------
% 5.55/1.67 % (771324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771324)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771324)Termination reason: Instruction limit
% 5.55/1.67 % (771324)Termination phase: Saturation
% 5.55/1.67 % (771324)Time elapsed: 0.004 s
% 5.55/1.67 % (771324)Peak memory usage: 88 MB
% 5.55/1.67 % (771324)Instructions burned: 6 (million)
% 5.55/1.67 % (771325)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1513392161:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.55/1.67 % (771323)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3149580317:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.55/1.67 % (771326)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1898009509:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.55/1.67 % (771321)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4192975130:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.55/1.67 % (771322)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1753341230:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.55/1.67 % (771320)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4286948577:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.55/1.67 % (771323)First to succeed.
% 5.55/1.67 % (771323)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-771315"
% 5.55/1.67 % (771320)Instruction limit reached!
% 5.55/1.67 % (771320)------------------------------
% 5.55/1.67 % (771320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771320)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771320)Termination reason: Instruction limit
% 5.55/1.67 % (771320)Termination phase: Saturation
% 5.55/1.67 % (771320)Time elapsed: 0.043 s
% 5.55/1.67 % (771320)Peak memory usage: 115 MB
% 5.55/1.67 % (771320)Instructions burned: 12 (million)
% 5.55/1.67 % (771326)Instruction limit reached!
% 5.55/1.67 % (771326)------------------------------
% 5.55/1.67 % (771326)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771326)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771326)Termination reason: Instruction limit
% 5.55/1.67 % (771326)Termination phase: Saturation
% 5.55/1.67 % (771326)Time elapsed: 0.070 s
% 5.55/1.67 % (771326)Peak memory usage: 118 MB
% 5.55/1.67 % (771326)Instructions burned: 33 (million)
% 5.55/1.67 % (771325)Instruction limit reached!
% 5.55/1.67 % (771325)------------------------------
% 5.55/1.67 % (771325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771325)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771325)Termination reason: Instruction limit
% 5.55/1.67 % (771325)Termination phase: Saturation
% 5.55/1.67 % (771325)Time elapsed: 0.072 s
% 5.55/1.67 % (771325)Peak memory usage: 115 MB
% 5.55/1.67 % (771325)Instructions burned: 46 (million)
% 5.55/1.67 % (771328)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3574216160:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 5.55/1.67 % (771328)Instruction limit reached!
% 5.55/1.67 % (771328)------------------------------
% 5.55/1.67 % (771328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771328)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771328)Termination reason: Instruction limit
% 5.55/1.67 % (771328)Termination phase: Saturation
% 5.55/1.67 % (771328)Time elapsed: 0.017 s
% 5.55/1.67 % (771328)Peak memory usage: 88 MB
% 5.55/1.67 % (771328)Instructions burned: 14 (million)
% 5.55/1.67 % (771322)Instruction limit reached!
% 5.55/1.67 % (771322)------------------------------
% 5.55/1.67 % (771322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771322)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771322)Termination reason: Instruction limit
% 5.55/1.67 % (771322)Termination phase: Saturation
% 5.55/1.67 % (771322)Time elapsed: 0.238 s
% 5.55/1.67 % (771322)Peak memory usage: 118 MB
% 5.55/1.67 % (771322)Instructions burned: 201 (million)
% 5.55/1.67 % (771335)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=3894139014:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 5.55/1.67 % (771335)Instruction limit reached!
% 5.55/1.67 % (771335)------------------------------
% 5.55/1.67 % (771335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771335)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771335)Termination reason: Instruction limit
% 5.55/1.67 % (771335)Termination phase: Saturation
% 5.55/1.67 % (771335)Time elapsed: 0.017 s
% 5.55/1.67 % (771335)Peak memory usage: 88 MB
% 5.55/1.67 % (771335)Instructions burned: 30 (million)
% 5.55/1.67 % (771337)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=3919127829:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 5.55/1.67 % (771336)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3502459162:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 5.55/1.67 % (771321)Instruction limit reached!
% 5.55/1.67 % (771321)------------------------------
% 5.55/1.67 % (771321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771321)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771321)Termination reason: Instruction limit
% 5.55/1.67 % (771321)Termination phase: Saturation
% 5.55/1.67 % (771321)Time elapsed: 0.347 s
% 5.55/1.67 % (771321)Peak memory usage: 117 MB
% 5.55/1.67 % (771321)Instructions burned: 308 (million)
% 5.55/1.67 % (771336)Instruction limit reached!
% 5.55/1.67 % (771336)------------------------------
% 5.55/1.67 % (771336)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771336)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771336)Termination reason: Instruction limit
% 5.55/1.67 % (771336)Termination phase: Saturation
% 5.55/1.67 % (771336)Time elapsed: 0.016 s
% 5.55/1.67 % (771336)Peak memory usage: 90 MB
% 5.55/1.67 % (771336)Instructions burned: 16 (million)
% 5.55/1.67 % (771337)Instruction limit reached!
% 5.55/1.67 % (771337)------------------------------
% 5.55/1.67 % (771337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771337)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771337)Termination reason: Instruction limit
% 5.55/1.67 % (771337)Termination phase: Saturation
% 5.55/1.67 % (771337)Time elapsed: 0.031 s
% 5.55/1.67 % (771337)Peak memory usage: 89 MB
% 5.55/1.67 % (771337)Instructions burned: 26 (million)
% 5.55/1.67 % (771339)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=2882614956:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 5.55/1.67 % (771339)Also succeeded, but the first one will report.
% 5.55/1.67 % (771323)Refutation found. Thanks to Tanya!
% 5.55/1.67 % SZS status Theorem for theBenchmark
% 5.55/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 5.55/1.67 % (771323)------------------------------
% 5.55/1.67 % (771323)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.55/1.67 % (771323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.55/1.67 % (771323)CaDiCaL version: 2.1.3
% 5.55/1.67 % (771323)Termination reason: Refutation
% 5.55/1.67 % (771323)Time elapsed: 0.006 s
% 5.55/1.67 % (771323)Peak memory usage: 89 MB
% 5.55/1.67 % (771323)Instructions burned: 4 (million)
% 5.55/1.67 % (771323)------------------------------
% 5.55/1.67 % (771323)------------------------------
% 5.55/1.67 % (771315)Success in time 0.672 s
% 5.55/1.67 % Vampire exiting
%------------------------------------------------------------------------------