%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO554+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 01:21:27 PM UTC 2026
% Result : Theorem 54.75s 9.39s
% Output : CNFRefutation 54.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 12 unt; 0 def)
% Number of atoms : 171 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 158 ( 51 ~; 45 |; 50 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 16 ( 16 usr; 16 con; 0-0 aty)
% Number of variables : 310 ( 0 sgn 278 !; 32 ?; 83 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X0,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD1) ).
fof(f2,axiom,
! [X0,X1,X2] :
( coll(X0,X1,X2)
=> coll(X1,X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD2) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( coll(X0,X1,X3)
& coll(X0,X1,X2) )
=> coll(X2,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD3) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X2,X3)
=> perp(X2,X3,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD8) ).
fof(f9,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( perp(X2,X3,X4,X5)
& perp(X0,X1,X2,X3) )
=> para(X0,X1,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD9) ).
fof(f19,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD19) ).
fof(f20,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
=> eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD20) ).
fof(f39,axiom,
! [X0,X1,X2,X3,X4,X5] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
=> para(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD39) ).
fof(f40,axiom,
! [X0,X1,X2,X3,X4,X5] :
( para(X0,X1,X2,X3)
=> eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD40) ).
fof(f67,axiom,
! [X0,X1,X2] :
( para(X0,X1,X0,X2)
=> coll(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO012+0.ax',ruleD66) ).
fof(f95,conjecture,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ( circle(X1,X2,X6,X15)
& circle(X0,X2,X6,X14)
& circle(X1,X2,X5,X13)
& coll(X1,X4,X5)
& circle(X1,X2,X4,X12)
& coll(X2,X3,X4)
& circle(X0,X2,X3,X11)
& circle(X1,X2,X9,X10)
& circle(X0,X2,X7,X8)
& perp(X2,X0,X2,X1) )
=> coll(X3,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL012014) ).
fof(f96,negated_conjecture,
~ ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ( circle(X1,X2,X6,X15)
& circle(X0,X2,X6,X14)
& circle(X1,X2,X5,X13)
& coll(X1,X4,X5)
& circle(X1,X2,X4,X12)
& coll(X2,X3,X4)
& circle(X0,X2,X3,X11)
& circle(X1,X2,X9,X10)
& circle(X0,X2,X7,X8)
& perp(X2,X0,X2,X1) )
=> coll(X3,X5,X6) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(flattening,[],[f100]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(ennf_transformation,[],[f9]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(flattening,[],[f108]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(ennf_transformation,[],[f19]) ).
fof(f124,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(ennf_transformation,[],[f39]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(ennf_transformation,[],[f40]) ).
fof(f197,plain,
! [X0,X1,X2] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(ennf_transformation,[],[f67]) ).
fof(f249,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( circle(X1,X2,X6,X15)
& circle(X0,X2,X6,X14)
& circle(X1,X2,X5,X13)
& coll(X1,X4,X5)
& circle(X1,X2,X4,X12)
& coll(X2,X3,X4)
& circle(X0,X2,X3,X11)
& circle(X1,X2,X9,X10)
& circle(X0,X2,X7,X8)
& perp(X2,X0,X2,X1)
& ~ coll(X3,X5,X6) ),
inference(ennf_transformation,[],[f96]) ).
fof(f250,plain,
? [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( circle(X1,X2,X6,X15)
& circle(X0,X2,X6,X14)
& circle(X1,X2,X5,X13)
& coll(X1,X4,X5)
& circle(X1,X2,X4,X12)
& coll(X2,X3,X4)
& circle(X0,X2,X3,X11)
& circle(X1,X2,X9,X10)
& circle(X0,X2,X7,X8)
& perp(X2,X0,X2,X1)
& ~ coll(X3,X5,X6) ),
inference(flattening,[],[f249]) ).
fof(f270,plain,
( circle(sK21,sK22,sK26,sK35)
& circle(sK20,sK22,sK26,sK34)
& circle(sK21,sK22,sK25,sK33)
& coll(sK21,sK24,sK25)
& circle(sK21,sK22,sK24,sK32)
& coll(sK22,sK23,sK24)
& circle(sK20,sK22,sK23,sK31)
& circle(sK21,sK22,sK29,sK30)
& circle(sK20,sK22,sK27,sK28)
& perp(sK22,sK20,sK22,sK21)
& ~ coll(sK23,sK25,sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24,sK25,sK26,sK27,sK28,sK29,sK30,sK31,sK32,sK33,sK34,sK35]),skolemize(X0,sK20),skolemize(X1,sK21),skolemize(X2,sK22),skolemize(X3,sK23),skolemize(X4,sK24),skolemize(X5,sK25),skolemize(X6,sK26),skolemize(X7,sK27),skolemize(X8,sK28),skolemize(X9,sK29),skolemize(X10,sK30),skolemize(X11,sK31),skolemize(X12,sK32),skolemize(X13,sK33),skolemize(X14,sK34),skolemize(X15,sK35)],[f250]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X0,X2,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f272,plain,
! [X2,X0,X1] :
( ~ coll(X0,X1,X2)
| coll(X1,X0,X2) ),
inference(cnf_transformation,[],[f99]) ).
fof(f273,plain,
! [X2,X3,X0,X1] :
( ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2)
| coll(X2,X3,X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ perp(X0,X1,X2,X3)
| perp(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f279,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3)
| para(X0,X1,X4,X5) ),
inference(cnf_transformation,[],[f109]) ).
fof(f289,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X2,X3,X0,X1,X6,X7,X4,X5) ),
inference(cnf_transformation,[],[f123]) ).
fof(f290,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7)
| eqangle(X4,X5,X6,X7,X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f124]) ).
fof(f309,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ para(X0,X1,X2,X3)
| eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f149]) ).
fof(f337,plain,
! [X2,X0,X1] :
( ~ para(X0,X1,X0,X2)
| coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f197]) ).
fof(f393,plain,
perp(sK22,sK20,sK22,sK21),
inference(cnf_transformation,[],[f270]) ).
fof(f394,plain,
~ coll(sK23,sK25,sK26),
inference(cnf_transformation,[],[f270]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[],[f273]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f279]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( para(X0,X1,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X2,X3) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[],[f337]) ).
tcf(c_162,negated_conjecture,
~ coll(sK23,sK25,sK26),
inference(cnf_transformation,[],[f394]) ).
tcf(c_163,negated_conjecture,
perp(sK22,sK20,sK22,sK21),
inference(cnf_transformation,[],[f393]) ).
tcf(c_25572,plain,
perp(sK22,sK21,sK22,sK20),
inference(superposition,[status(thm)],[c_163,c_56]) ).
tcf(c_25876,plain,
! [X0: $i,X1: $i] :
( para(sK22,sK21,X0,X1)
| ~ perp(sK22,sK20,X0,X1) ),
inference(superposition,[status(thm)],[c_25572,c_57]) ).
tcf(c_25993,plain,
para(sK22,sK21,sK22,sK21),
inference(superposition,[status(thm)],[c_163,c_25876]) ).
tcf(c_26143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X2,X3,X4,X5,X0,X1,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_88,c_68]) ).
tcf(c_26941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( eqangle(X4,X5,X2,X3,X4,X5,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(superposition,[status(thm)],[c_26143,c_67]) ).
tcf(c_32656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( para(X2,X3,X2,X3)
| ~ para(X0,X1,X0,X1) ),
inference(superposition,[status(thm)],[c_26941,c_87]) ).
tcf(c_32801,plain,
! [X0: $i,X1: $i] : para(X0,X1,X0,X1),
inference(superposition,[status(thm)],[c_25993,c_32656]) ).
tcf(c_32846,plain,
! [X0: $i,X1: $i] : coll(X0,X1,X1),
inference(superposition,[status(thm)],[c_32801,c_115]) ).
tcf(c_32857,plain,
! [X0: $i,X1: $i] : coll(X0,X1,X0),
inference(superposition,[status(thm)],[c_32846,c_50]) ).
tcf(c_32994,plain,
! [X0: $i,X1: $i] : coll(X0,X0,X1),
inference(superposition,[status(thm)],[c_32857,c_49]) ).
tcf(c_33118,plain,
! [X0: $i,X1: $i,X2: $i] :
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(superposition,[status(thm)],[c_32994,c_51]) ).
tcf(c_33121,plain,
! [X0: $i,X1: $i,X2: $i] : coll(X0,X1,X2),
inference(forward_subsumption_resolution,[status(thm)],[c_33118,c_32994]) ).
tcf(c_33122,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_162,c_33121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO554+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 12:23:19 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 54.75/9.39 % SZS status Started for theBenchmark.p
% 54.75/9.39 % SZS status Theorem for theBenchmark.p
% 54.75/9.39
% 54.75/9.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 54.75/9.39
% 54.75/9.39 % ------ iProver source info
% 54.75/9.39
% 54.75/9.39 % git: date: 2026-07-19 20:42:38 +0200
% 54.75/9.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 54.75/9.39 % git: non_committed_changes: false
% 54.75/9.39
% 54.75/9.39 % ------ Parsing...
% 54.75/9.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 54.75/9.39
% 54.75/9.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 54.75/9.39
% 54.75/9.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 54.75/9.39
% 54.75/9.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 54.75/9.39 % ------ Proving...
% 54.75/9.39 % ------ Problem Properties
% 54.75/9.39
% 54.75/9.39 %
% 54.75/9.39 % clauses 123
% 54.75/9.39 % conjectures 11
% 54.75/9.39 % EPR 86
% 54.75/9.39 % Horn 113
% 54.75/9.39 % unary 11
% 54.75/9.39 % binary 37
% 54.75/9.39 % lits 339
% 54.75/9.39 % lits eq 4
% 54.75/9.39 % fd_pure 0
% 54.75/9.39 % fd_pseudo 0
% 54.75/9.39 % fd_cond 0
% 54.75/9.39 % fd_pseudo_cond 4
% 54.75/9.39 % AC symbols 0
% 54.75/9.39
% 54.75/9.39 % ------ Input Options Time Limit: Unbounded
% 54.75/9.39
% 54.75/9.39
% 54.75/9.39 % ------
% 54.75/9.39 % Current options:
% 54.75/9.39 % ------
% 54.75/9.39
% 54.75/9.39
% 54.75/9.39 %
% 54.75/9.39
% 54.75/9.39 % ------ Proving...
% 54.75/9.39 %
% 54.75/9.39
% 54.75/9.39 % SZS status Theorem for theBenchmark.p
% 54.75/9.39
% 54.75/9.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 54.75/9.39
% 54.75/9.39
%------------------------------------------------------------------------------