%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV672+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n014.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 : Sun Sep 27 08:48:20 AM UTC 2026
% Result : Theorem 9.31s 3.24s
% Output : Refutation 9.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 48 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 128 ( 58 equ; 0 cnn)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 472 ( 6 ~; 16 |; 40 &; 386 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 7 con; 0-4 aty)
% Number of variables : 94 ( 0 ^; 66 !; 28 ?; 94 :)
% Comments :
%------------------------------------------------------------------------------
thf(cPLF_2eSmallstep_2emulti___24a4_decl,type,
cPLF_2eSmallstep_2emulti___24a4: $i > $i > $i > $i > $o ).
thf(cStlc_2eSTLC_2etm_decl,type,
cStlc_2eSTLC_2etm: $i ).
thf(cStlc_2eSTLC_2estep_decl,type,
cStlc_2eSTLC_2estep: $i ).
thf(cStlc_2eSTLC_2eapp___24a2_decl,type,
cStlc_2eSTLC_2eapp___24a2: $i > $i > $i ).
thf(cStlc_2eSTLC_2eabs___24a3_decl,type,
cStlc_2eSTLC_2eabs___24a3: $i > $i > $i > $i ).
thf(cStlc_2eSTLC_2ex_decl,type,
cStlc_2eSTLC_2ex: $i ).
thf(cStlc_2eSTLC_2eArrow___24a2_decl,type,
cStlc_2eSTLC_2eArrow___24a2: $i > $i > $i ).
thf(cStlc_2eSTLC_2eBool_decl,type,
cStlc_2eSTLC_2eBool: $i ).
thf(cStlc_2eSTLC_2evar___24a1_decl,type,
cStlc_2eSTLC_2evar___24a1: $i > $i ).
thf(cStlc_2eSTLC_2evalue___24a1_decl,type,
cStlc_2eSTLC_2evalue___24a1: $i > $o ).
thf(cStlc_2eSTLC_2efls_decl,type,
cStlc_2eSTLC_2efls: $i ).
thf(cCoq_2eStrings_2eString_2estring___24t_decl,type,
cCoq_2eStrings_2eString_2estring___24t: $i > $o ).
thf(cStlc_2eSTLC_2ety___24t_decl,type,
cStlc_2eSTLC_2ety___24t: $i > $o ).
thf(cStlc_2eSTLC_2etm___24t_decl,type,
cStlc_2eSTLC_2etm___24t: $i > $o ).
thf(cStlc_2eSTLC_2etru_decl,type,
cStlc_2eSTLC_2etru: $i ).
thf(cStlc_2eSTLC_2etest___24a3_decl,type,
cStlc_2eSTLC_2etest___24a3: $i > $i > $i > $i ).
thf(cType___24t_decl,type,
cType___24t: $i > $o ).
thf(19,axiom,
! [A: $i,B: $i] :
( cStlc_2eSTLC_2eBool
!= ( B @ ( A @ cStlc_2eSTLC_2eArrow___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Stlc.STLC.Bool$Stlc.STLC.Arrow') ).
thf(120,plain,
! [A: $i,B: $i] :
( cStlc_2eSTLC_2eBool
!= ( B @ ( A @ cStlc_2eSTLC_2eArrow___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
cStlc_2eSTLC_2etm @ cType___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Stlc.STLC.tm') ).
thf(125,plain,
cStlc_2eSTLC_2etm @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( A @ cStlc_2eSTLC_2eabs___24a3 ) ) )
= ( F @ ( D @ ( B @ cStlc_2eSTLC_2eabs___24a3 ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Stlc.STLC.abs') ).
thf(106,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( A @ cStlc_2eSTLC_2eabs___24a3 ) ) )
= ( F @ ( D @ ( B @ cStlc_2eSTLC_2eabs___24a3 ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cStlc_2eSTLC_2ety___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( A
= ( C @ ( B @ cStlc_2eSTLC_2eArrow___24a2 ) ) )
& ( C @ cStlc_2eSTLC_2ety___24t ) )
& ( B @ cStlc_2eSTLC_2ety___24t ) )
| ( A = cStlc_2eSTLC_2eBool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Stlc.STLC.ty') ).
thf(132,plain,
! [A: $i] :
( ( A @ cStlc_2eSTLC_2ety___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ( A
= ( C @ ( B @ cStlc_2eSTLC_2eArrow___24a2 ) ) )
& ( C @ cStlc_2eSTLC_2ety___24t ) )
& ( B @ cStlc_2eSTLC_2ety___24t ) )
| ( A = cStlc_2eSTLC_2eBool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.step_example2') ).
thf(124,plain,
cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ cStlc_2eSTLC_2etest___24a3 ) ) @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.step_example4') ).
thf(105,plain,
cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ cStlc_2eSTLC_2etest___24a3 ) ) @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cCoq_2eStrings_2eString_2estring___24t )
=> ! [B: $i] :
( ( B @ cStlc_2eSTLC_2ety___24t )
=> ! [C: $i] :
( ( C @ cStlc_2eSTLC_2etm___24t )
=> ( C @ ( B @ ( A @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2evalue___24a1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.v_abs') ).
thf(27,plain,
! [A: $i] :
( ( A @ cCoq_2eStrings_2eString_2estring___24t )
=> ! [B: $i] :
( ( B @ cStlc_2eSTLC_2ety___24t )
=> ! [C: $i] :
( ( C @ cStlc_2eSTLC_2etm___24t )
=> ( C @ ( B @ ( A @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2evalue___24a1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ cStlc_2eSTLC_2eapp___24a2 ) )
= ( D @ ( B @ cStlc_2eSTLC_2eapp___24a2 ) ) )
=> ( ( A = B )
& ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Stlc.STLC.app') ).
thf(80,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ cStlc_2eSTLC_2eapp___24a2 ) )
= ( D @ ( B @ cStlc_2eSTLC_2eapp___24a2 ) ) )
=> ( ( A = B )
& ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
cStlc_2eSTLC_2ex @ cCoq_2eStrings_2eString_2estring___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Stlc.STLC.x') ).
thf(104,plain,
cStlc_2eSTLC_2ex @ cCoq_2eStrings_2eString_2estring___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,axiom,
cStlc_2eSTLC_2efls @ cStlc_2eSTLC_2evalue___24a1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.v_fls') ).
thf(26,plain,
cStlc_2eSTLC_2efls @ cStlc_2eSTLC_2evalue___24a1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
cStlc_2eSTLC_2etru @ cStlc_2eSTLC_2etm___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Stlc.STLC.tru') ).
thf(30,plain,
cStlc_2eSTLC_2etru @ cStlc_2eSTLC_2etm___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cStlc_2eSTLC_2etm___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ( B @ cStlc_2eSTLC_2etest___24a3 ) ) ) )
& ( D @ cStlc_2eSTLC_2etm___24t ) )
& ( C @ cStlc_2eSTLC_2etm___24t ) )
& ( B @ cStlc_2eSTLC_2etm___24t ) )
| ( A = cStlc_2eSTLC_2efls )
| ( A = cStlc_2eSTLC_2etru )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ( B @ cStlc_2eSTLC_2eabs___24a3 ) ) ) )
& ( D @ cStlc_2eSTLC_2etm___24t ) )
& ( C @ cStlc_2eSTLC_2ety___24t ) )
& ( B @ cCoq_2eStrings_2eString_2estring___24t ) )
| ? [B: $i] :
( ? [C: $i] :
( ( A
= ( C @ ( B @ cStlc_2eSTLC_2eapp___24a2 ) ) )
& ( C @ cStlc_2eSTLC_2etm___24t ) )
& ( B @ cStlc_2eSTLC_2etm___24t ) )
| ? [B: $i] :
( ( A
= ( B @ cStlc_2eSTLC_2evar___24a1 ) )
& ( B @ cCoq_2eStrings_2eString_2estring___24t ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Stlc.STLC.tm') ).
thf(42,plain,
! [A: $i] :
( ( A @ cStlc_2eSTLC_2etm___24t )
=> ( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ( B @ cStlc_2eSTLC_2etest___24a3 ) ) ) )
& ( D @ cStlc_2eSTLC_2etm___24t ) )
& ( C @ cStlc_2eSTLC_2etm___24t ) )
& ( B @ cStlc_2eSTLC_2etm___24t ) )
| ( A = cStlc_2eSTLC_2efls )
| ( A = cStlc_2eSTLC_2etru )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ( B @ cStlc_2eSTLC_2eabs___24a3 ) ) ) )
& ( D @ cStlc_2eSTLC_2etm___24t ) )
& ( C @ cStlc_2eSTLC_2ety___24t ) )
& ( B @ cCoq_2eStrings_2eString_2estring___24t ) )
| ? [B: $i] :
( ? [C: $i] :
( ( A
= ( C @ ( B @ cStlc_2eSTLC_2eapp___24a2 ) ) )
& ( C @ cStlc_2eSTLC_2etm___24t ) )
& ( B @ cStlc_2eSTLC_2etm___24t ) )
| ? [B: $i] :
( ( A
= ( B @ cStlc_2eSTLC_2evar___24a1 ) )
& ( B @ cCoq_2eStrings_2eString_2estring___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(25,plain,
~ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2ety___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Stlc.STLC.Bool') ).
thf(78,plain,
cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2ety___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
cStlc_2eSTLC_2etru @ cStlc_2eSTLC_2evalue___24a1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.v_tru') ).
thf(29,plain,
cStlc_2eSTLC_2etru @ cStlc_2eSTLC_2evalue___24a1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cStlc_2eSTLC_2etm___24t )
=> ( ( A @ cStlc_2eSTLC_2evalue___24a1 )
=> ( ( A = cStlc_2eSTLC_2efls )
| ( A = cStlc_2eSTLC_2etru )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ( B @ cStlc_2eSTLC_2eabs___24a3 ) ) ) )
& ( D @ cStlc_2eSTLC_2etm___24t ) )
& ( C @ cStlc_2eSTLC_2ety___24t ) )
& ( B @ cCoq_2eStrings_2eString_2estring___24t ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inversion_Stlc.STLC.value') ).
thf(32,plain,
! [A: $i] :
( ( A @ cStlc_2eSTLC_2etm___24t )
=> ( ( A @ cStlc_2eSTLC_2evalue___24a1 )
=> ( ( A = cStlc_2eSTLC_2efls )
| ( A = cStlc_2eSTLC_2etru )
| ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( A
= ( D @ ( C @ ( B @ cStlc_2eSTLC_2eabs___24a3 ) ) ) )
& ( D @ cStlc_2eSTLC_2etm___24t ) )
& ( C @ cStlc_2eSTLC_2ety___24t ) )
& ( B @ cCoq_2eStrings_2eString_2estring___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( A @ cStlc_2eSTLC_2etest___24a3 ) ) )
= ( F @ ( D @ ( B @ cStlc_2eSTLC_2etest___24a3 ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Stlc.STLC.test') ).
thf(64,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( C @ ( A @ cStlc_2eSTLC_2etest___24a3 ) ) )
= ( F @ ( D @ ( B @ cStlc_2eSTLC_2etest___24a3 ) ) ) )
=> ( ( A = B )
& ( C = D )
& ( E = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ( A @ cStlc_2eSTLC_2evar___24a1 )
= ( B @ cStlc_2eSTLC_2evar___24a1 ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Stlc.STLC.var') ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ( A @ cStlc_2eSTLC_2evar___24a1 )
= ( B @ cStlc_2eSTLC_2evar___24a1 ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(7,axiom,
cStlc_2eSTLC_2efls @ cStlc_2eSTLC_2etm___24t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Stlc.STLC.fls') ).
thf(31,plain,
cStlc_2eSTLC_2efls @ cStlc_2eSTLC_2etm___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ cStlc_2eSTLC_2etest___24a3 ) ) @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.step_example3') ).
thf(126,plain,
cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2etru @ ( cStlc_2eSTLC_2efls @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ cStlc_2eSTLC_2etest___24a3 ) ) @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(12,axiom,
cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Stlc.STLC.step_example1') ).
thf(79,plain,
cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2evar___24a1 @ ( cStlc_2eSTLC_2eBool @ ( cStlc_2eSTLC_2eBool @ cStlc_2eSTLC_2eArrow___24a2 ) @ ( cStlc_2eSTLC_2ex @ cStlc_2eSTLC_2eabs___24a3 ) ) @ cStlc_2eSTLC_2eapp___24a2 ) @ ( cStlc_2eSTLC_2estep @ ( cStlc_2eSTLC_2etm @ cPLF_2eSmallstep_2emulti___24a4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ cStlc_2eSTLC_2eArrow___24a2 ) )
= ( D @ ( B @ cStlc_2eSTLC_2eArrow___24a2 ) ) )
=> ( ( A = B )
& ( C = D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_Stlc.STLC.Arrow') ).
thf(90,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ cStlc_2eSTLC_2eArrow___24a2 ) )
= ( D @ ( B @ cStlc_2eSTLC_2eArrow___24a2 ) ) )
=> ( ( A = B )
& ( C = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ cStlc_2eSTLC_2evar___24a1 )
!= ( C @ ( B @ cStlc_2eSTLC_2eapp___24a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Stlc.STLC.var$Stlc.STLC.app') ).
thf(100,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ cStlc_2eSTLC_2evar___24a1 )
!= ( C @ ( B @ cStlc_2eSTLC_2eapp___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(140,plain,
$false,
inference(e,[status(thm)],[120,125,106,132,124,105,27,80,104,26,30,42,25,78,29,32,64,127,31,126,79,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV672+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.39 % Computer : n014.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 11:35:46 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.69/1.75 % [INFO] Parsing done (763ms).
% 3.69/1.77 % [INFO] Running in sequential loop mode.
% 4.61/2.06 % [INFO] eprover registered as external prover.
% 4.61/2.06 % [INFO] Scanning for conjecture ...
% 5.22/2.26 % [INFO] Found a conjecture (or negated_conjecture) and 3118 axioms. Running axiom selection ...
% 5.68/2.39 % [INFO] Axiom selection finished. Selected 22 axioms (removed 3096 axioms).
% 6.17/2.43 % [INFO] Problem is first-order (TPTP FOF).
% 6.17/2.44 % [INFO] Type checking passed.
% 6.17/2.44 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 9.31/3.23 % External prover 'e' found a proof!
% 9.31/3.23 % [INFO] Killing All external provers ...
% 9.31/3.24 % Time passed: 2698ms (effective reasoning time: 1461ms)
% 9.31/3.24 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.31/3.24 % Axioms used in derivation (22): $_inj_Stlc.STLC.var, $_inj_Stlc.STLC.app, $_inj_Stlc.STLC.abs, Stlc.STLC.step_example4, $_typeof_Stlc.STLC.tm, $_discrim_Stlc.STLC.var$Stlc.STLC.app, Stlc.STLC.v_fls, $_typeof_Stlc.STLC.x, Stlc.STLC.step_example3, $_inversion_Stlc.STLC.ty, $_discrim_Stlc.STLC.Bool$Stlc.STLC.Arrow, Stlc.STLC.step_example2, $_typeof_Stlc.STLC.tru, Stlc.STLC.v_abs, Stlc.STLC.step_example1, $_typeof_Stlc.STLC.fls, $_inj_Stlc.STLC.Arrow, $_inj_Stlc.STLC.test, $_typeof_Stlc.STLC.Bool, Stlc.STLC.v_tru, $_inversion_Stlc.STLC.tm, $_inversion_Stlc.STLC.value
% 9.31/3.24 % No. of inferences in proof: 48
% 9.31/3.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2698 ms resp. 1461 ms w/o parsing
% 9.76/3.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.76/3.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------