%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n008.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 02:56:25 PM UTC 2026
% Result : Theorem 2.05s 1.28s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 12 unt; 3 def)
% Number of atoms : 133 ( 115 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 132 ( 56 ~; 48 |; 14 &)
% ( 6 <=>; 8 =>; 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; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 110 !; 18 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,conjecture,
! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_mcart_1) ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( pair_second(ordered_pair(X0,X1)) = X1
& pair_first(ordered_pair(X0,X1)) = X0 ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_first(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_mcart_1) ).
fof(f20,axiom,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X1] :
( X1 = pair_second(X0)
<=> ! [X2,X3] :
( X0 = ordered_pair(X2,X3)
=> X1 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_mcart_1) ).
fof(f21,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X4 ) ) ),
inference(rectify,[],[f19]) ).
fof(f22,plain,
! [X0] :
( ? [X1,X2] : X0 = ordered_pair(X1,X2)
=> ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) = X0
=> X3 = X5 ) ) ),
inference(rectify,[],[f20]) ).
fof(f30,plain,
? [X0,X1] :
( pair_second(ordered_pair(X0,X1)) != X1
| pair_first(ordered_pair(X0,X1)) != X0 ),
inference(ennf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( pair_first(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X4 ) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( pair_second(X0) = X3
<=> ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X5 ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f36,plain,
( sK4 != pair_second(ordered_pair(sK3,sK4))
| sK3 != pair_first(ordered_pair(sK3,sK4)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f30]) ).
fof(f37,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( ( pair_first(X0) != X3
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X4 ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X0
& X3 != X4 )
| pair_first(X0) = X3 ) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f38,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_first(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X4 ) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X0
& X1 != X2 )
| pair_first(X0) = X1 ) ) ),
inference(rectify,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_first(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X4 ) )
& ( ( ordered_pair(sK5(X0,X1),sK6(X0,X1)) = X0
& sK5(X0,X1) != X1 )
| pair_first(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1))],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1,X2] : ordered_pair(X1,X2) != X0
| ! [X3] :
( ( pair_second(X0) != X3
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X3 = X5 ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X0
& X3 != X5 )
| pair_second(X0) = X3 ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f41,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_second(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X5 ) )
& ( ? [X2,X3] :
( ordered_pair(X2,X3) = X0
& X1 != X3 )
| pair_second(X0) = X1 ) ) ),
inference(rectify,[],[f40]) ).
fof(f42,plain,
! [X0] :
( ! [X6,X7] : ordered_pair(X6,X7) != X0
| ! [X1] :
( ( pair_second(X0) != X1
| ! [X4,X5] :
( ordered_pair(X4,X5) != X0
| X1 = X5 ) )
& ( ( ordered_pair(sK7(X0,X1),sK8(X0,X1)) = X0
& sK8(X0,X1) != X1 )
| pair_second(X0) = X1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X2,sK7(X0,X1)),skolemize(X3,sK8(X0,X1))],[f41]) ).
fof(f54,plain,
( sK4 != pair_second(ordered_pair(sK3,sK4))
| sK3 != pair_first(ordered_pair(sK3,sK4)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0,X1,X6,X7,X4,X5] :
( ordered_pair(X6,X7) != X0
| pair_first(X0) != X1
| ordered_pair(X4,X5) != X0
| X1 = X4 ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1,X6,X7,X4,X5] :
( ordered_pair(X6,X7) != X0
| pair_second(X0) != X1
| ordered_pair(X4,X5) != X0
| X1 = X5 ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X1,X6,X7,X4,X5] :
( ordered_pair(X4,X5) != ordered_pair(X6,X7)
| pair_first(ordered_pair(X4,X5)) != X1
| X1 = X4 ),
inference(equality_resolution,[],[f55]) ).
fof(f64,plain,
! [X6,X7,X4,X5] :
( ordered_pair(X4,X5) != ordered_pair(X6,X7)
| pair_first(ordered_pair(X4,X5)) = X4 ),
inference(equality_resolution,[],[f63]) ).
fof(f67,plain,
! [X1,X6,X7,X4,X5] :
( ordered_pair(X4,X5) != ordered_pair(X6,X7)
| pair_second(ordered_pair(X4,X5)) != X1
| X1 = X5 ),
inference(equality_resolution,[],[f58]) ).
fof(f68,plain,
! [X6,X7,X4,X5] :
( ordered_pair(X4,X5) != ordered_pair(X6,X7)
| pair_second(ordered_pair(X4,X5)) = X5 ),
inference(equality_resolution,[],[f67]) ).
tcf(c_60,negated_conjecture,
( ( pair_second(ordered_pair(sK3,sK4)) != sK4 )
| ( pair_first(ordered_pair(sK3,sK4)) != sK3 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( pair_first(ordered_pair(X0,X1)) = X0 )
| ( ordered_pair(X0,X1) != ordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( pair_second(ordered_pair(X0,X1)) = X1 )
| ( ordered_pair(X0,X1) != ordered_pair(X2,X3) ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_344,definition,
iPr_def_10 = ordered_pair(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_345,definition,
iPr_def_11 = pair_first(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_346,definition,
iPr_def_12 = pair_second(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_347,negated_conjecture,
( ( iPr_def_12 != sK4 )
| ( iPr_def_11 != sK3 ) ),
inference(demodulation,[status(thm)],[c_60,c_346,c_344,c_345]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i] : pair_first(ordered_pair(X0,X1)) = X0,
inference(equality_resolution,[status(thm)],[c_63]) ).
tcf(c_661,plain,
pair_first(iPr_def_10) = sK3,
inference(superposition,[status(thm)],[c_344,c_656]) ).
tcf(c_662,plain,
sK3 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_661,c_345]) ).
tcf(c_663,plain,
ordered_pair(iPr_def_11,sK4) = iPr_def_10,
inference(demodulation,[status(thm)],[c_344,c_662]) ).
tcf(c_664,plain,
( ( iPr_def_11 != iPr_def_11 )
| ( sK4 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_347,c_662]) ).
tcf(c_665,plain,
sK4 != iPr_def_12,
inference(equality_resolution_simp,[status(thm)],[c_664]) ).
tcf(c_720,plain,
! [X0: $i,X1: $i] : pair_second(ordered_pair(X0,X1)) = X1,
inference(equality_resolution,[status(thm)],[c_66]) ).
tcf(c_763,plain,
pair_second(iPr_def_10) = sK4,
inference(superposition,[status(thm)],[c_663,c_720]) ).
tcf(c_764,plain,
sK4 = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_763,c_346]) ).
tcf(c_765,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_764,c_665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU267+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n008.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
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Thu Sep 24 13:28:54 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.41 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
% 0.02/0.42
% 0.02/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.42
% 0.02/0.42 % Detected problem language: tptp
% 0.02/0.43 % Proving...
% 2.05/1.28 % SZS status Started for theBenchmark.p
% 2.05/1.28 % SZS status Theorem for theBenchmark.p
% 2.05/1.28
% 2.05/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.05/1.28
% 2.05/1.28 % ------ iProver source info
% 2.05/1.28
% 2.05/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.05/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.05/1.28 % git: non_committed_changes: false
% 2.05/1.28
% 2.05/1.28 % ------ Parsing...
% 2.05/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.05/1.28 % ------ Proving...
% 2.05/1.28 % ------ Problem Properties
% 2.05/1.28
% 2.05/1.28 %
% 2.05/1.28 % clauses 19
% 2.05/1.28 % conjectures 1
% 2.05/1.28 % EPR 8
% 2.05/1.28 % Horn 16
% 2.05/1.28 % unary 7
% 2.05/1.28 % binary 11
% 2.05/1.28 % lits 32
% 2.05/1.28 % lits eq 19
% 2.05/1.28 % fd_pure 0
% 2.05/1.28 % fd_pseudo 0
% 2.05/1.28 % fd_cond 1
% 2.05/1.28 % fd_pseudo_cond 5
% 2.05/1.28 % AC symbols 0
% 2.05/1.28
% 2.05/1.28 % ------ Schedule dynamic 5 is on
% 2.05/1.28
% 2.05/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 % ------
% 2.05/1.28 % Current options:
% 2.05/1.28 % ------
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % ------ Proving...
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % SZS status Theorem for theBenchmark.p
% 2.05/1.28
% 2.05/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.05/1.28
% 2.05/1.28
%------------------------------------------------------------------------------