%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GEO523+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 01:21:23 PM UTC 2026
% Result : Theorem 11.05s 2.62s
% Output : CNFRefutation 11.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 38 unt; 0 def)
% Number of atoms : 143 ( 67 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 113 ( 47 ~; 59 |; 7 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 153 ( 0 sgn 149 !; 4 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
fof(f93,axiom,
! [X0,X1,X2] :
( s_m(X2,X1,X0)
| ~ s_m(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_2) ).
fof(f98,axiom,
! [X0,X1,X2] :
( X2 = s(X1,X0)
| ~ s_m(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_6) ).
fof(f99,axiom,
! [X0,X1] : s(X0,s(X0,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
fof(f103,axiom,
! [X0,X1] :
( X1 != X0
| s(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_10b) ).
fof(f104,axiom,
! [X0,X1,X2] : s_e(X0,X1,s(X2,X0),s(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_13) ).
fof(f118,axiom,
! [X0,X1,X2] :
( s_r(X2,X1,X0)
| ~ s_r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_2) ).
fof(f123,axiom,
! [X0,X1,X2] :
( X1 = X2
| ~ s_r(X0,X2,X1)
| ~ s_r(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_7) ).
fof(f146,axiom,
! [X0,X1] : s_m(X0,midpoint(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz8_22) ).
fof(f154,axiom,
! [X0,X1,X2,X3] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aExtPerp4) ).
fof(f184,axiom,
! [X0,X1,X2] :
( ( perp(X0,X1,X2,reflect(X0,X1,X2))
| X2 = reflect(X0,X1,X2)
| X0 = X1 )
& ( s_col(X0,X1,midpoint(X2,reflect(X0,X1,X2)))
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_2a) ).
fof(f185,axiom,
! [X0,X1,X2,X3] :
( ( X3 = reflect(X0,X1,X2)
| X2 != X3
| ~ s_col(X0,X1,midpoint(X2,X3))
| X0 = X1 )
& ( X3 = reflect(X0,X1,X2)
| ~ perp(X0,X1,X2,X3)
| ~ s_col(X0,X1,midpoint(X2,X3))
| X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_2b) ).
fof(f186,conjecture,
! [X0,X1,X2,X3] :
( reflect(X0,X1,X3) = X2
| reflect(X0,X1,X2) != X3
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz10_4) ).
fof(f187,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( reflect(X0,X1,X3) = X2
| reflect(X0,X1,X2) != X3
| X0 = X1 ),
inference(negated_conjecture,[status(cth)],[f186]) ).
fof(f198,axiom,
! [X0,X1,X2] :
( ( ~ s_e(X0,X2,X0,s(X1,X2))
| s_r(X0,X1,X2) )
& ( s_e(X0,X2,X0,s(X1,X2))
| ~ s_r(X0,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_Defn8_1) ).
fof(f203,plain,
? [X0,X1,X2,X3] :
( reflect(X0,X1,X3) != X2
& reflect(X0,X1,X2) = X3
& X0 != X1 ),
inference(ennf_transformation,[],[f187]) ).
fof(f204,plain,
( sK2 != reflect(sK0,sK1,sK3)
& sK3 = reflect(sK0,sK1,sK2)
& sK0 != sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f203]) ).
fof(f205,plain,
sK2 != reflect(sK0,sK1,sK3),
inference(cnf_transformation,[],[f204]) ).
fof(f206,plain,
sK3 = reflect(sK0,sK1,sK2),
inference(cnf_transformation,[],[f204]) ).
fof(f207,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f204]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( reflect(X0,X1,X2) = X3
| ~ perp(X0,X1,X2,X3)
| ~ s_col(X0,X1,midpoint(X2,X3))
| X0 = X1 ),
inference(cnf_transformation,[],[f185]) ).
fof(f225,plain,
! [X2,X0,X1] :
( perp(X0,X1,X2,reflect(X0,X1,X2))
| reflect(X0,X1,X2) = X2
| X0 = X1 ),
inference(cnf_transformation,[],[f184]) ).
fof(f226,plain,
! [X2,X0,X1] :
( s_col(X0,X1,midpoint(X2,reflect(X0,X1,X2)))
| X0 = X1 ),
inference(cnf_transformation,[],[f184]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f154]) ).
fof(f263,plain,
! [X0,X1] : s_m(X0,midpoint(X0,X1),X1),
inference(cnf_transformation,[],[f146]) ).
fof(f283,plain,
! [X2,X0,X1] :
( s(X1,X0) = X2
| ~ s_m(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f288,plain,
! [X2,X0,X1] :
( s_m(X2,X1,X0)
| ~ s_m(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f289,plain,
! [X2,X0,X1] :
( ~ s_e(X0,X2,X0,s(X1,X2))
| s_r(X0,X1,X2) ),
inference(cnf_transformation,[],[f198]) ).
fof(f305,plain,
! [X2,X0,X1] : s_e(X0,X1,s(X2,X0),s(X2,X1)),
inference(cnf_transformation,[],[f104]) ).
fof(f306,plain,
! [X0,X1] :
( X0 != X1
| s(X0,X1) = X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f310,plain,
! [X0,X1] : s(X0,s(X0,X1)) = X1,
inference(cnf_transformation,[],[f99]) ).
fof(f316,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ s_r(X0,X2,X1)
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[],[f123]) ).
fof(f320,plain,
! [X2,X0,X1] :
( s_r(X2,X1,X0)
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[],[f118]) ).
fof(f361,plain,
! [X1] : s(X1,X1) = X1,
inference(equality_resolution,[],[f306]) ).
tcf(c_49,negated_conjecture,
sK0 != sK1,
inference(cnf_transformation,[],[f207]) ).
tcf(c_50,negated_conjecture,
reflect(sK0,sK1,sK2) = sK3,
inference(cnf_transformation,[],[f206]) ).
tcf(c_51,negated_conjecture,
reflect(sK0,sK1,sK3) != sK2,
inference(cnf_transformation,[],[f205]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X1 )
| ( reflect(X0,X1,X2) = X3 )
| ~ perp(X0,X1,X2,X3)
| ~ s_col(X0,X1,midpoint(X2,X3)) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( s_col(X0,X1,midpoint(X2,reflect(X0,X1,X2)))
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( perp(X0,X1,X2,reflect(X0,X1,X2))
| ( X0 = X1 )
| ( reflect(X0,X1,X2) = X2 ) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] : s_m(X0,midpoint(X0,X1),X1),
inference(cnf_transformation,[],[f263]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( s(X1,X0) = X2 )
| ~ s_m(X0,X1,X2) ),
inference(cnf_transformation,[],[f283]) ).
tcf(c_132,plain,
! [X0: $i,X1: $i,X2: $i] :
( s_m(X2,X1,X0)
| ~ s_m(X0,X1,X2) ),
inference(cnf_transformation,[],[f288]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( s_r(X0,X2,X1)
| ~ s_e(X0,X1,X0,s(X2,X1)) ),
inference(cnf_transformation,[],[f289]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : s_e(X0,X1,s(X2,X0),s(X2,X1)),
inference(cnf_transformation,[],[f305]) ).
tcf(c_150,plain,
! [X0: $i] : s(X0,X0) = X0,
inference(cnf_transformation,[],[f361]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : s(X0,s(X0,X1)) = X1,
inference(cnf_transformation,[],[f310]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ s_r(X0,X2,X1)
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[],[f316]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( s_r(X2,X1,X0)
| ~ s_r(X0,X1,X2) ),
inference(cnf_transformation,[],[f320]) ).
tcf(c_5583,plain,
! [X0: $i,X1: $i] : s_m(X0,midpoint(X1,X0),X1),
inference(superposition,[status(thm)],[c_107,c_132]) ).
tcf(c_5587,plain,
! [X0: $i,X1: $i] : s_e(X0,X1,X0,s(X0,X1)),
inference(superposition,[status(thm)],[c_150,c_149]) ).
tcf(c_5665,plain,
! [X0: $i,X1: $i] : s_e(X0,s(X0,X1),X0,X1),
inference(superposition,[status(thm)],[c_154,c_5587]) ).
tcf(c_5921,plain,
! [X0: $i,X1: $i] : s(midpoint(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_107,c_127]) ).
tcf(c_5925,plain,
! [X0: $i,X1: $i] : s(midpoint(X0,X1),X1) = X0,
inference(superposition,[status(thm)],[c_5583,c_127]) ).
tcf(c_5965,plain,
! [X0: $i,X1: $i] : s_e(midpoint(X0,X1),X1,midpoint(X0,X1),X0),
inference(superposition,[status(thm)],[c_5921,c_5665]) ).
tcf(c_5966,plain,
! [X0: $i,X1: $i] : s_e(midpoint(X0,X1),X0,midpoint(X0,X1),X1),
inference(superposition,[status(thm)],[c_5921,c_5587]) ).
tcf(c_6234,plain,
( s_col(sK0,sK1,midpoint(sK2,sK3))
| ( sK0 = sK1 ) ),
inference(superposition,[status(thm)],[c_50,c_69]) ).
tcf(c_6240,plain,
s_col(sK0,sK1,midpoint(sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_6234,c_49]) ).
tcf(c_6332,plain,
! [X0: $i,X1: $i] : s_r(midpoint(s(X0,X1),X1),X0,X1),
inference(superposition,[status(thm)],[c_5965,c_134]) ).
tcf(c_6511,plain,
! [X0: $i,X1: $i] : s_r(midpoint(X0,X1),midpoint(X1,X0),X1),
inference(superposition,[status(thm)],[c_5921,c_6332]) ).
tcf(c_6538,plain,
! [X0: $i,X1: $i] : s_r(X0,midpoint(X0,X1),midpoint(X1,X0)),
inference(superposition,[status(thm)],[c_6511,c_164]) ).
tcf(c_6747,plain,
! [X0: $i,X1: $i] : s_r(midpoint(X0,s(X1,X0)),X1,X0),
inference(superposition,[status(thm)],[c_5966,c_134]) ).
tcf(c_6752,plain,
! [X0: $i,X1: $i] : s_r(midpoint(X0,X1),midpoint(X1,X0),X0),
inference(superposition,[status(thm)],[c_5925,c_6747]) ).
tcf(c_6762,plain,
! [X0: $i,X1: $i] : s_r(X0,midpoint(X1,X0),midpoint(X0,X1)),
inference(superposition,[status(thm)],[c_6752,c_164]) ).
tcf(c_6886,plain,
! [X0: $i,X1: $i] :
( ( midpoint(X0,X1) = midpoint(X1,X0) )
| ~ s_r(X0,midpoint(X0,X1),midpoint(X1,X0)) ),
inference(superposition,[status(thm)],[c_6762,c_160]) ).
tcf(c_6895,plain,
! [X0: $i,X1: $i] : midpoint(X0,X1) = midpoint(X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_6886,c_6538]) ).
tcf(c_6920,plain,
s_col(sK0,sK1,midpoint(sK3,sK2)),
inference(demodulation,[status(thm)],[c_6240,c_6895]) ).
tcf(c_11274,plain,
( perp(sK0,sK1,sK2,sK3)
| ( sK0 = sK1 )
| ( reflect(sK0,sK1,sK2) = sK2 ) ),
inference(superposition,[status(thm)],[c_50,c_70]) ).
tcf(c_11282,plain,
( perp(sK0,sK1,sK2,sK3)
| ( sK3 = sK2 )
| ( sK0 = sK1 ) ),
inference(light_normalisation,[status(thm)],[c_11274,c_50]) ).
tcf(c_11283,plain,
( perp(sK0,sK1,sK2,sK3)
| ( sK3 = sK2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11282,c_49]) ).
tcf(c_11345,plain,
( perp(sK0,sK1,sK3,sK2)
| ( sK3 = sK2 ) ),
inference(superposition,[status(thm)],[c_11283,c_99]) ).
tcf(c_15401,plain,
( ( sK0 = sK1 )
| ( reflect(sK0,sK1,sK3) = sK2 )
| ~ perp(sK0,sK1,sK3,sK2) ),
inference(superposition,[status(thm)],[c_6920,c_67]) ).
tcf(c_15414,plain,
~ perp(sK0,sK1,sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_15401,c_49,c_51]) ).
tcf(c_15494,plain,
sK3 = sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_11345,c_15414]) ).
tcf(c_15559,plain,
reflect(sK0,sK1,sK3) != sK3,
inference(demodulation,[status(thm)],[c_51,c_15494]) ).
tcf(c_15560,plain,
reflect(sK0,sK1,sK3) = sK3,
inference(demodulation,[status(thm)],[c_50,c_15494]) ).
tcf(c_15561,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15559,c_15560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO523+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.60 % Computer : n014.cluster.edu
% 0.13/0.60 % Model : x86_64 x86_64
% 0.13/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.60 % Memory : 8046.5625MB
% 0.13/0.60 % OS : Linux 6.8.0-71-generic
% 0.13/0.61 % CPULimit : 300
% 0.13/0.61 % WCLimit : 300
% 0.13/0.61 % DateTime : Wed Sep 23 12:18:04 UTC 2026
% 0.13/0.61 % CPUTime :
% 0.13/0.61 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.67 Running first-order theorem proving
% 0.16/0.67 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
% 0.16/0.68
% 0.16/0.68 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.68
% 0.16/0.68 % Detected problem language: tptp
% 0.16/0.70 % Proving...
% 11.05/2.62 % SZS status Started for theBenchmark.p
% 11.05/2.62 % SZS status Theorem for theBenchmark.p
% 11.05/2.62
% 11.05/2.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.05/2.62
% 11.05/2.62 % ------ iProver source info
% 11.05/2.62
% 11.05/2.62 % git: date: 2026-07-19 20:42:38 +0200
% 11.05/2.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.05/2.62 % git: non_committed_changes: false
% 11.05/2.62
% 11.05/2.62 % ------ Parsing...
% 11.05/2.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.05/2.62
% 11.05/2.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 11 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 11.05/2.62
% 11.05/2.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.05/2.62
% 11.05/2.62 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.05/2.62 % ------ Proving...
% 11.05/2.62 % ------ Problem Properties
% 11.05/2.62
% 11.05/2.62 %
% 11.05/2.62 % clauses 128
% 11.05/2.62 % conjectures 3
% 11.05/2.62 % EPR 101
% 11.05/2.62 % Horn 92
% 11.05/2.62 % unary 19
% 11.05/2.62 % binary 45
% 11.05/2.62 % lits 399
% 11.05/2.62 % lits eq 85
% 11.05/2.62 % fd_pure 0
% 11.05/2.62 % fd_pseudo 0
% 11.05/2.62 % fd_cond 0
% 11.05/2.62 % fd_pseudo_cond 48
% 11.05/2.62 % AC symbols 0
% 11.05/2.62
% 11.05/2.62 % ------ Schedule dynamic 5 is on
% 11.05/2.62
% 11.05/2.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 11.05/2.62
% 11.05/2.62
% 11.05/2.62 % ------
% 11.05/2.62 % Current options:
% 11.05/2.62 % ------
% 11.05/2.62
% 11.05/2.62
% 11.05/2.62 %
% 11.05/2.62
% 11.05/2.62 % ------ Proving...
% 11.05/2.62 %
% 11.05/2.62
% 11.05/2.62 % SZS status Theorem for theBenchmark.p
% 11.05/2.62
% 11.05/2.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.05/2.63
% 11.05/2.63
%------------------------------------------------------------------------------