%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO083+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 : Fri Sep 25 01:19:49 PM UTC 2026
% Result : Theorem 3.12s 31.02s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 6 unt; 0 def)
% Number of atoms : 171 ( 12 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 193 ( 69 ~; 78 |; 39 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 116 ( 0 sgn 103 !; 13 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',part_of_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( X0 = sum(X1,X2)
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',sum_defn) ).
fof(f17,conjecture,
! [X0,X1,X2,X3] :
( ( meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) )
=> part_of(sum(X0,X1),sum(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2) )
=> part_of(sum(X0,X1),sum(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
? [X0,X1,X2,X3] :
( meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& ~ part_of(sum(X0,X1),sum(X0,X2)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f20,plain,
? [X0,X1,X2,X3] :
( meet(X3,X0,X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& ~ part_of(sum(X0,X1),sum(X0,X2)) ),
inference(flattening,[],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f33,plain,
( meet(sK3,sK0,sK2)
& meet(sK3,sK0,sK1)
& part_of(sK1,sK2)
& ~ part_of(sum(sK0,sK1),sum(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X3] :
( ( ~ incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| incident_c(X3,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X3] :
( ( ~ incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| incident_c(X3,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X4] :
( ( ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) )
& ( ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) )
| incident_c(X4,X0) ) ) )
& ( ? [X3] :
( ( incident_c(X3,X0)
| incident_c(X3,X2)
| incident_c(X3,X1) )
& ( ~ incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) != X0
| ! [X4] :
( ( ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) )
& ( ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) )
| incident_c(X4,X0) ) ) )
& ( ( ( incident_c(sK5(X0,X1,X2),X0)
| incident_c(sK5(X0,X1,X2),X2)
| incident_c(sK5(X0,X1,X2),X1) )
& ( ~ incident_c(sK5(X0,X1,X2),X0)
| ( ~ incident_c(sK5(X0,X1,X2),X2)
& ~ incident_c(sK5(X0,X1,X2),X1) ) ) )
| X0 = sum(X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f38]) ).
fof(f44,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X2] :
( ~ incident_c(X2,X1)
| incident_c(X2,X0) ) )
& ( ? [X2] :
( incident_c(X2,X1)
& ~ incident_c(X2,X0) )
| part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f26]) ).
fof(f45,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ? [X2] :
( incident_c(X2,X1)
& ~ incident_c(X2,X0) )
| part_of(X1,X0) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( ( ~ part_of(X1,X0)
| ! [X3] :
( ~ incident_c(X3,X1)
| incident_c(X3,X0) ) )
& ( ( incident_c(sK8(X0,X1),X1)
& ~ incident_c(sK8(X0,X1),X0) )
| part_of(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X0,X1))],[f45]) ).
fof(f56,plain,
part_of(sK1,sK2),
inference(cnf_transformation,[],[f33]) ).
fof(f57,plain,
~ part_of(sum(sK0,sK1),sum(sK0,sK2)),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X0)
| incident_c(X4,X2)
| incident_c(X4,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X2)
| incident_c(X4,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
! [X2,X0,X1,X4] :
( sum(X1,X2) != X0
| ~ incident_c(X4,X1)
| incident_c(X4,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f74,plain,
! [X3,X0,X1] :
( ~ part_of(X1,X0)
| ~ incident_c(X3,X1)
| incident_c(X3,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f75,plain,
! [X0,X1] :
( incident_c(sK8(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f76,plain,
! [X0,X1] :
( ~ incident_c(sK8(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f89,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,X1)
| incident_c(X4,sum(X1,X2)) ),
inference(equality_resolution,[],[f61]) ).
fof(f90,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,X2)
| incident_c(X4,sum(X1,X2)) ),
inference(equality_resolution,[],[f60]) ).
fof(f91,plain,
! [X2,X1,X4] :
( ~ incident_c(X4,sum(X1,X2))
| incident_c(X4,X2)
| incident_c(X4,X1) ),
inference(equality_resolution,[],[f59]) ).
tcf(c_49,negated_conjecture,
~ part_of(sum(sK0,sK1),sum(sK0,sK2)),
inference(cnf_transformation,[],[f57]) ).
tcf(c_50,negated_conjecture,
part_of(sK1,sK2),
inference(cnf_transformation,[],[f56]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,sum(X1,X2))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,sum(X2,X1))
| ~ incident_c(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X0,X2)
| incident_c(X0,X1)
| ~ incident_c(X0,sum(X1,X2)) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| ~ incident_c(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( part_of(X1,X0)
| incident_c(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( incident_c(X2,X1)
| ~ incident_c(X2,X0)
| ~ part_of(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_1475,plain,
! [X0: $i,X1: $i,X2: $i] :
( part_of(X2,sum(X0,X1))
| ~ incident_c(sK8(sum(X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_58,c_69]) ).
tcf(c_1514,plain,
! [X0: $i] :
( incident_c(X0,sK2)
| ~ incident_c(X0,sK1) ),
inference(superposition,[status(thm)],[c_50,c_71]) ).
tcf(c_1523,plain,
! [X0: $i] :
( part_of(sK1,X0)
| incident_c(sK8(X0,sK1),sK2) ),
inference(superposition,[status(thm)],[c_70,c_1514]) ).
tcf(c_1553,plain,
! [X0: $i,X1: $i,X2: $i] :
( part_of(sum(X1,X2),X0)
| incident_c(sK8(X0,sum(X1,X2)),X2)
| incident_c(sK8(X0,sum(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_70,c_59]) ).
tcf(c_1785,plain,
( part_of(sum(sK0,sK1),sum(sK0,sK2))
| ~ incident_c(sK8(sum(sK0,sK2),sum(sK0,sK1)),sum(sK0,sK2)) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_1836,plain,
! [X0: $i] : part_of(sK1,sum(X0,sK2)),
inference(superposition,[status(thm)],[c_1523,c_1475]) ).
tcf(c_2132,plain,
! [X0: $i,X1: $i] :
( incident_c(X0,sum(X1,sK2))
| ~ incident_c(X0,sK1) ),
inference(superposition,[status(thm)],[c_1836,c_71]) ).
tcf(c_2171,plain,
! [X0: $i,X1: $i] :
( part_of(X1,sum(X0,sK2))
| ~ incident_c(sK8(sum(X0,sK2),X1),sK1) ),
inference(superposition,[status(thm)],[c_2132,c_69]) ).
tcf(c_3631,plain,
! [X0: $i] :
( incident_c(sK8(sum(sK0,sK2),sum(sK0,sK1)),sum(sK0,X0))
| ~ incident_c(sK8(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_7259,plain,
! [X0: $i,X1: $i] :
( part_of(sum(X1,sK1),sum(X0,sK2))
| incident_c(sK8(sum(X0,sK2),sum(X1,sK1)),X1) ),
inference(superposition,[status(thm)],[c_1553,c_2171]) ).
tcf(c_7429,plain,
( part_of(sum(sK0,sK1),sum(sK0,sK2))
| incident_c(sK8(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_7259]) ).
tcf(c_12783,plain,
( incident_c(sK8(sum(sK0,sK2),sum(sK0,sK1)),sum(sK0,sK2))
| ~ incident_c(sK8(sum(sK0,sK2),sum(sK0,sK1)),sK0) ),
inference(instantiation,[status(thm)],[c_3631]) ).
tcf(c_12784,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_12783,c_7429,c_1785,c_49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/30.34 % Computer : n012.cluster.edu
% 0.04/30.34 % Model : x86_64 x86_64
% 0.04/30.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/30.34 % Memory : 8046.5625MB
% 0.04/30.34 % OS : Linux 6.8.0-71-generic
% 0.04/30.34 % CPULimit : 300
% 0.04/30.34 % WCLimit : 300
% 0.04/30.34 % DateTime : Wed Sep 23 10:46:14 UTC 2026
% 0.04/30.34 % CPUTime :
% 0.04/30.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/30.36 Running first-order theorem proving
% 0.04/30.36 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/30.37
% 0.04/30.37 % ======== iProver multi-core TPTP/SMT =========
% 0.04/30.37
% 0.04/30.37 % Detected problem language: tptp
% 0.04/30.37 % Proving...
% 3.12/31.02 % SZS status Started for theBenchmark.p
% 3.12/31.02 % SZS status Theorem for theBenchmark.p
% 3.12/31.02
% 3.12/31.02 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.12/31.02
% 3.12/31.02 % ------ iProver source info
% 3.12/31.02
% 3.12/31.02 % git: date: 2026-07-19 20:42:38 +0200
% 3.12/31.02 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.12/31.02 % git: non_committed_changes: false
% 3.12/31.02
% 3.12/31.02 % ------ Parsing...
% 3.12/31.02 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.12/31.02
% 3.12/31.02 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.12/31.02
% 3.12/31.02 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.12/31.02
% 3.12/31.02 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.12/31.02 % ------ Proving...
% 3.12/31.02 % ------ Problem Properties
% 3.12/31.02
% 3.12/31.02 %
% 3.12/31.02 % clauses 35
% 3.12/31.02 % conjectures 4
% 3.12/31.02 % EPR 12
% 3.12/31.02 % Horn 22
% 3.12/31.02 % unary 4
% 3.12/31.02 % binary 10
% 3.12/31.02 % lits 110
% 3.12/31.02 % lits eq 10
% 3.12/31.02 % fd_pure 0
% 3.12/31.02 % fd_pseudo 0
% 3.12/31.02 % fd_cond 0
% 3.12/31.02 % fd_pseudo_cond 6
% 3.12/31.02 % AC symbols 0
% 3.12/31.02
% 3.12/31.02 % ------ Schedule dynamic 5 is on
% 3.12/31.02
% 3.12/31.02 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.12/31.02
% 3.12/31.02
% 3.12/31.02 % ------
% 3.12/31.02 % Current options:
% 3.12/31.02 % ------
% 3.12/31.02
% 3.12/31.02
% 3.12/31.02 %
% 3.12/31.02
% 3.12/31.02 % ------ Proving...
% 3.12/31.02 %
% 3.12/31.02
% 3.12/31.02 % SZS status Theorem for theBenchmark.p
% 3.12/31.02
% 3.12/31.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.12/31.02
% 3.12/31.02
%------------------------------------------------------------------------------