%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n006.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 03:38:56 PM UTC 2026
% Result : Unsatisfiable 1.46s 6.29s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 117 ( 1 unt; 0 def)
% Number of atoms : 597 ( 0 equ)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 383 ( 178 ~; 205 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 280 ( 0 sgn 280 !; 0 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,negated_conjecture,
! [X2,X0,X1] :
( q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_2) ).
fof(f3,negated_conjecture,
! [X0,X1] :
( ~ s(X1,X1)
| ~ s(X0,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_3) ).
fof(f5,negated_conjecture,
! [X2,X3,X0,X1] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f9,negated_conjecture,
! [X2,X0,X1] :
( ~ s(X1,X1)
| ~ q(X2,X2)
| p(f1(X0,X1),f1(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f11,negated_conjecture,
! [X2,X0,X1] :
( q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1))
| ~ p(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
fof(f12,negated_conjecture,
! [X0,X1] :
( ~ s(X1,X1)
| ~ s(X0,f1(X0,X1))
| ~ p(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
fof(f14,negated_conjecture,
! [X2,X3,X0,X1] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| ~ p(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
fof(f15,negated_conjecture,
! [X2,X0,X1] :
( ~ s(X1,X1)
| s(f1(X0,X1),X2)
| ~ p(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
fof(f16,negated_conjecture,
! [X2,X0,X1] :
( ~ q(X2,f1(X0,X2))
| ~ q(X1,X1)
| ~ p(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f18,negated_conjecture,
! [X2,X0,X1] :
( ~ s(X2,X2)
| ~ q(X1,X1)
| ~ p(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_18) ).
fof(f19,negated_conjecture,
! [X2,X0,X1] :
( ~ q(X2,f1(X1,X2))
| ~ s(X1,f1(X1,X2))
| s(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_19) ).
fof(f20,negated_conjecture,
! [X2,X3,X0,X1] :
( q(f1(X1,X2),X3)
| ~ s(X1,f1(X1,X2))
| s(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_20) ).
fof(f21,negated_conjecture,
! [X2,X0,X1] :
( ~ s(X2,X2)
| ~ s(X1,f1(X1,X2))
| s(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_21) ).
fof(f25,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ q(X3,f1(X1,X3))
| ~ q(X2,X2)
| s(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_25) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1))
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_78,negated_conjecture,
! [X0: $i,X1: $i] :
( p(f1(X0,X1),f1(X0,X1))
| ~ s(X1,X1)
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_84,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( p(f1(X2,X0),f1(X2,X0))
| ~ q(X1,X1)
| ~ s(X0,X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_86,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(X0,X1),X2)
| ~ p(X0,X0)
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_87,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ s(X1,X1)
| ~ p(X0,X0)
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_89,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| ~ p(X0,X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_90,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(f1(X0,X1),X2)
| ~ s(X1,X1)
| ~ p(X0,X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ q(X2,X2)
| ~ p(X1,X1)
| ~ q(X0,f1(X1,X0)) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_93,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ q(X2,X2)
| ~ s(X1,X1)
| ~ p(X0,X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_94,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X0)
| ~ q(X1,f1(X0,X1))
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_95,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(X3,X0)
| q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X0)
| ~ s(X1,X1)
| ~ s(X0,f1(X0,X1)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_100,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(X3,X1)
| ~ q(X2,X2)
| ~ q(X0,f1(X1,X0)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( ~ q(X1,X1)
| ~ s(X0,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_84,c_93]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ s(X2,X2)
| ~ s(X1,X1)
| ~ s(X0,f1(X0,X1))
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(resolution,[status(thm)],[c_78,c_87]) ).
tcf(c_403,plain,
( ~ s(iProver_bot,iProver_bot)
| ~ s(iProver_bot,f1(iProver_bot,iProver_bot))
| ~ s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_402]) ).
tcf(c_1758,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ q(X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_137]) ).
tcf(c_1759,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ s(X0,X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_137]) ).
tcf(c_1760,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_137]) ).
tcf(c_1761,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_12
| s(X2,X1)
| ~ q(X0,f1(X1,X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_100]) ).
tcf(c_1762,negated_conjecture,
( iPr_def_12
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_100]) ).
tcf(c_1763,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ~ p(X1,X1)
| ~ q(X0,f1(X1,X0)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_91]) ).
tcf(c_1764,negated_conjecture,
( iPr_def_13
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_91]) ).
tcf(c_1767,plain,
( iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_1760]) ).
tcf(c_1768,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ s(X0,X0) ),
inference(demodulation,[status(thm)],[c_1759]) ).
tcf(c_1771,negated_conjecture,
( iPr_def_12
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_1762]) ).
tcf(c_1772,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X1)
| ~ iPr_def_12
| ~ q(X0,f1(X1,X0)) ),
inference(demodulation,[status(thm)],[c_1761]) ).
tcf(c_1777,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X0)
| ~ s(X1,X1)
| ~ s(X0,f1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_1778,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(X3,X0)
| q(f1(X0,X1),X2)
| ~ s(X0,f1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_1779,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X0)
| ~ q(X1,f1(X0,X1))
| ~ s(X0,f1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_1781,negated_conjecture,
( iPr_def_13
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_1764]) ).
tcf(c_1782,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_13
| ~ p(X1,X1)
| ~ q(X0,f1(X1,X0)) ),
inference(demodulation,[status(thm)],[c_1763]) ).
tcf(c_1784,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(f1(X0,X1),X2)
| ~ s(X1,X1)
| ~ p(X0,X0) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_1785,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| ~ p(X0,X0) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_1788,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(X0,X1),X2)
| ~ p(X0,X0)
| ~ s(X0,f1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_1793,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ q(X0,X0) ),
inference(demodulation,[status(thm)],[c_1758]) ).
tcf(c_1795,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(X0,X1),X3)
| s(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_1798,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1))
| ~ s(X0,f1(X0,X1)) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_1801,plain,
( ~ iPr_def_11
| ~ s(iProver_bot,iProver_bot) ),
inference(instantiation,[status(thm)],[c_1768]) ).
tcf(c_1822,plain,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(X0,X1),f1(X2,f1(X0,X1)))
| ~ p(X0,X0)
| ~ s(X0,f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1788]) ).
tcf(c_1823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(X3,X0)
| q(f1(X0,X1),f1(X2,f1(X0,X1)))
| ~ s(X0,f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1778]) ).
tcf(c_1833,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10
| ~ q(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1793]) ).
tcf(c_1834,plain,
! [X0: $i,X1: $i] :
( q(f1(X0,X1),f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1))
| ~ s(X0,f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1798]) ).
tcf(c_1835,plain,
! [X0: $i,X1: $i] :
( q(f1(X0,X1),f1(X0,X1))
| ~ p(X0,X0)
| ~ s(X0,f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1788]) ).
tcf(c_1836,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X0)
| q(f1(X0,X1),f1(X0,X1))
| ~ s(X0,f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1778]) ).
tcf(c_1837,plain,
( ~ iPr_def_10
| ~ q(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_1833]) ).
tcf(c_1838,plain,
( s(iProver_bot,iProver_bot)
| q(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| ~ s(iProver_bot,f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_1836]) ).
tcf(c_1840,plain,
( q(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| ~ s(iProver_bot,f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_1834]) ).
tcf(c_1847,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(f1(X0,X1),X2)
| q(f1(X0,X1),f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1795]) ).
tcf(c_1848,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(f1(X0,X1),X2)
| q(f1(X0,X1),f1(X0,X1))
| ~ p(X0,X0) ),
inference(instantiation,[status(thm)],[c_1785]) ).
tcf(c_1857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(X3,f1(X0,X1))
| q(f1(f1(X0,X1),X2),f1(f1(X0,X1),X2))
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_1836]) ).
tcf(c_1863,plain,
( s(iProver_bot,f1(iProver_bot,iProver_bot))
| q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot))
| ~ s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_1857]) ).
tcf(c_1877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(f1(X0,X1),X3)
| p(f1(X0,X1),f1(X0,X1))
| q(f1(X0,X1),f1(X2,f1(X0,X1))) ),
inference(instantiation,[status(thm)],[c_1795]) ).
tcf(c_1878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(f1(X0,X1),X3)
| q(f1(X0,X1),f1(X2,f1(X0,X1)))
| ~ p(X0,X0) ),
inference(instantiation,[status(thm)],[c_1785]) ).
tcf(c_1899,plain,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(X0,X1),f1(X0,X1))
| s(f1(X0,X1),f1(f1(X0,X1),X2))
| ~ p(X0,X0) ),
inference(instantiation,[status(thm)],[c_1848]) ).
tcf(c_1901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( s(X4,f1(X0,X1))
| q(f1(f1(X0,X1),X2),f1(X3,f1(f1(X0,X1),X2)))
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_1823]) ).
tcf(c_1906,plain,
( s(iProver_bot,f1(iProver_bot,iProver_bot))
| q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(iProver_bot,f1(f1(iProver_bot,iProver_bot),iProver_bot)))
| ~ s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_1901]) ).
tcf(c_1975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(X0,X1),f1(X3,f1(X0,X1)))
| s(f1(X0,X1),f1(f1(X0,X1),X2))
| ~ p(X0,X0) ),
inference(instantiation,[status(thm)],[c_1878]) ).
tcf(c_1993,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(f1(X0,X1),f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1))
| q(f1(X0,X1),f1(X2,f1(X0,X1))) ),
inference(instantiation,[status(thm)],[c_1877]) ).
tcf(c_1994,plain,
( s(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| q(f1(iProver_bot,iProver_bot),f1(iProver_bot,f1(iProver_bot,iProver_bot))) ),
inference(instantiation,[status(thm)],[c_1993]) ).
tcf(c_2142,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10
| ~ q(f1(f1(X0,X1),X2),f1(f1(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_1833]) ).
tcf(c_2143,plain,
( ~ iPr_def_10
| ~ q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2142]) ).
tcf(c_2155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( s(X5,f1(X0,X1))
| q(f1(f1(X0,X1),X2),f1(f1(X3,X4),f1(f1(X0,X1),X2)))
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_1901]) ).
tcf(c_2191,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ~ s(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1768]) ).
tcf(c_2192,plain,
( ~ iPr_def_11
| ~ s(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2191]) ).
tcf(c_2206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( s(X4,X3)
| ~ iPr_def_12
| ~ q(f1(f1(X0,X1),X2),f1(X3,f1(f1(X0,X1),X2))) ),
inference(instantiation,[status(thm)],[c_1772]) ).
tcf(c_2207,plain,
( s(iProver_bot,iProver_bot)
| ~ iPr_def_12
| ~ q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(iProver_bot,f1(f1(iProver_bot,iProver_bot),iProver_bot))) ),
inference(instantiation,[status(thm)],[c_2206]) ).
tcf(c_2241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(f1(X0,X1),X2),f1(f1(X0,X1),X2))
| s(f1(f1(X0,X1),X2),f1(f1(f1(X0,X1),X2),X3))
| ~ p(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1899]) ).
tcf(c_2243,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( q(f1(f1(X0,X1),X2),f1(X3,f1(f1(X0,X1),X2)))
| ~ p(f1(X0,X1),f1(X0,X1))
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_1822]) ).
tcf(c_2244,plain,
! [X0: $i,X1: $i,X2: $i] :
( q(f1(f1(X0,X1),X2),f1(f1(X0,X1),X2))
| ~ p(f1(X0,X1),f1(X0,X1))
| ~ s(f1(X0,X1),f1(f1(X0,X1),X2)) ),
inference(instantiation,[status(thm)],[c_1835]) ).
tcf(c_2247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(f1(f1(X0,X1),X2),X3)
| ~ s(X2,X2)
| ~ p(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1784]) ).
tcf(c_2252,plain,
( q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(iProver_bot,f1(f1(iProver_bot,iProver_bot),iProver_bot)))
| ~ p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| ~ s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2243]) ).
tcf(c_2254,plain,
( q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot))
| s(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot))
| ~ p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2241]) ).
tcf(c_2256,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_13
| ~ q(X2,f1(f1(X0,X1),X2))
| ~ p(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1782]) ).
tcf(c_2315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( q(f1(f1(X0,X1),X2),f1(X4,f1(f1(X0,X1),X2)))
| s(f1(f1(X0,X1),X2),f1(f1(f1(X0,X1),X2),X3))
| ~ p(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_1975]) ).
tcf(c_2316,plain,
( q(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(iProver_bot,f1(f1(iProver_bot,iProver_bot),iProver_bot)))
| s(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot))
| ~ p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2315]) ).
tcf(c_2497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ iPr_def_13
| ~ p(f1(X3,X4),f1(X3,X4))
| ~ q(f1(f1(X0,X1),X2),f1(f1(X3,X4),f1(f1(X0,X1),X2))) ),
inference(instantiation,[status(thm)],[c_2256]) ).
tcf(c_2522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(f1(X0,X1),f1(f1(X0,X1),X2))
| ~ s(X3,X3)
| ~ s(f1(f1(X0,X1),X2),f1(f1(f1(X0,X1),X2),X3)) ),
inference(instantiation,[status(thm)],[c_1777]) ).
tcf(c_2523,plain,
( s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot))
| ~ s(iProver_bot,iProver_bot)
| ~ s(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2522]) ).
tcf(c_2527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(f1(f1(X0,X1),X2),f1(f1(f1(X0,X1),X2),X3))
| ~ s(X2,X2)
| ~ p(f1(X0,X1),f1(X0,X1)) ),
inference(instantiation,[status(thm)],[c_2247]) ).
tcf(c_2529,plain,
( s(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot))
| ~ s(iProver_bot,iProver_bot)
| ~ p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2527]) ).
tcf(c_2536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(f1(X0,X1),f1(f1(X0,X1),X2))
| q(f1(f1(f1(X0,X1),X2),X3),f1(f1(f1(X0,X1),X2),X3))
| ~ s(f1(f1(X0,X1),X2),f1(f1(f1(X0,X1),X2),X3)) ),
inference(instantiation,[status(thm)],[c_1857]) ).
tcf(c_2537,plain,
( s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot))
| q(f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot))
| ~ s(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2536]) ).
tcf(c_2546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( s(f1(X0,X1),f1(f1(X0,X1),X2))
| q(f1(f1(f1(X0,X1),X2),X3),f1(f1(X4,X5),f1(f1(f1(X0,X1),X2),X3)))
| ~ s(f1(f1(X0,X1),X2),f1(f1(f1(X0,X1),X2),X3)) ),
inference(instantiation,[status(thm)],[c_2155]) ).
tcf(c_2547,plain,
( s(f1(iProver_bot,iProver_bot),f1(f1(iProver_bot,iProver_bot),iProver_bot))
| q(f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot),f1(f1(iProver_bot,iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot)))
| ~ s(f1(f1(iProver_bot,iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_2546]) ).
tcf(c_3648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ iPr_def_10
| ~ q(f1(f1(f1(X0,X1),X2),X3),f1(f1(f1(X0,X1),X2),X3)) ),
inference(instantiation,[status(thm)],[c_2142]) ).
tcf(c_3649,plain,
( ~ iPr_def_10
| ~ q(f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot)) ),
inference(instantiation,[status(thm)],[c_3648]) ).
tcf(c_3695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ iPr_def_13
| ~ p(f1(X4,X5),f1(X4,X5))
| ~ q(f1(f1(f1(X0,X1),X2),X3),f1(f1(X4,X5),f1(f1(f1(X0,X1),X2),X3))) ),
inference(instantiation,[status(thm)],[c_2497]) ).
tcf(c_3696,plain,
( ~ iPr_def_13
| ~ p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| ~ q(f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot),f1(f1(iProver_bot,iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot))) ),
inference(instantiation,[status(thm)],[c_3695]) ).
tcf(c_4320,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( s(X6,f1(X4,X5))
| ~ iPr_def_12
| ~ q(f1(f1(f1(X0,X1),X2),X3),f1(f1(X4,X5),f1(f1(f1(X0,X1),X2),X3))) ),
inference(instantiation,[status(thm)],[c_2206]) ).
tcf(c_4321,plain,
( s(iProver_bot,f1(iProver_bot,iProver_bot))
| ~ iPr_def_12
| ~ q(f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot),f1(f1(iProver_bot,iProver_bot),f1(f1(f1(iProver_bot,iProver_bot),iProver_bot),iProver_bot))) ),
inference(instantiation,[status(thm)],[c_4320]) ).
tcf(c_4507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( s(X3,X2)
| ~ iPr_def_12
| ~ q(f1(X0,X1),f1(X2,f1(X0,X1))) ),
inference(instantiation,[status(thm)],[c_1772]) ).
tcf(c_4510,plain,
( s(iProver_bot,iProver_bot)
| ~ iPr_def_12
| ~ q(f1(iProver_bot,iProver_bot),f1(iProver_bot,f1(iProver_bot,iProver_bot))) ),
inference(instantiation,[status(thm)],[c_4507]) ).
tcf(c_4679,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,X0)
| ~ s(X0,f1(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_1779,c_1767,c_1771,c_1781,c_1801,c_1833,c_1834,c_1994,c_2142,c_2192,c_2207,c_2244,c_2252,c_2241,c_2316,c_2536,c_2547,c_3648,c_3696,c_4510]) ).
tcf(c_4681,plain,
( s(iProver_bot,iProver_bot)
| ~ s(iProver_bot,f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_4679]) ).
tcf(c_4757,plain,
! [X0: $i,X1: $i,X2: $i] :
( p(f1(X0,X1),f1(X0,X1))
| s(f1(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_1795,c_1767,c_1771,c_1801,c_1833,c_1847,c_1906,c_1994,c_2142,c_2192,c_2207,c_2244,c_2241,c_2316,c_2536,c_2547,c_3648,c_4321,c_4510,c_4681]) ).
tcf(c_4758,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( s(f1(X0,X1),X2)
| p(f1(X0,X1),f1(X0,X1)) ),
inference(renaming,[status(thm)],[c_4757]) ).
tcf(c_4764,plain,
! [X0: $i,X1: $i,X2: $i] :
( s(X2,f1(X0,X1))
| p(f1(X0,X1),f1(X0,X1)) ),
inference(superposition,[status(thm)],[c_4758,c_4679]) ).
tcf(c_4766,plain,
! [X0: $i,X1: $i] :
( p(f1(X0,X1),f1(X0,X1))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_4758,c_1768]) ).
tcf(c_4774,plain,
( p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot))
| ~ iPr_def_11 ),
inference(instantiation,[status(thm)],[c_4766]) ).
tcf(c_4776,plain,
( s(iProver_bot,f1(iProver_bot,iProver_bot))
| p(f1(iProver_bot,iProver_bot),f1(iProver_bot,iProver_bot)) ),
inference(instantiation,[status(thm)],[c_4764]) ).
tcf(c_4850,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4776,c_4774,c_3696,c_3649,c_2547,c_2537,c_2529,c_2523,c_2316,c_2254,c_2252,c_2207,c_2143,c_1863,c_1840,c_1838,c_1837,c_1801,c_1781,c_1771,c_1767,c_403]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 23:55:20 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.41 Running first-order theorem proving
% 0.14/5.41 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
% 0.14/5.42
% 0.14/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42
% 0.14/5.42 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 1.46/6.29 % SZS status Started for theBenchmark.p
% 1.46/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.46/6.29
% 1.46/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.46/6.29
% 1.46/6.29 % ------ iProver source info
% 1.46/6.29
% 1.46/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.46/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.46/6.29 % git: non_committed_changes: false
% 1.46/6.29
% 1.46/6.29 % ------ Parsing...% successful
% 1.46/6.29
% 1.46/6.29
% 1.46/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.46/6.29
% 1.46/6.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.46/6.29
% 1.46/6.29 % ------ Preprocessing... gs_s sp: 8 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.46/6.29 % ------ Proving...
% 1.46/6.29 % ------ Problem Properties
% 1.46/6.29
% 1.46/6.29 %
% 1.46/6.29 % clauses 30
% 1.46/6.29 % conjectures 27
% 1.46/6.29 % EPR 6
% 1.46/6.29 % Horn 15
% 1.46/6.29 % unary 0
% 1.46/6.29 % binary 6
% 1.46/6.29 % lits 84
% 1.46/6.29 % lits eq 0
% 1.46/6.29 % fd_pure 0
% 1.46/6.29 % fd_pseudo 0
% 1.46/6.29 % fd_cond 0
% 1.46/6.29 % fd_pseudo_cond 0
% 1.46/6.29 % AC symbols 0
% 1.46/6.29
% 1.46/6.29 % ------ Schedule dynamic 5 is on
% 1.46/6.29
% 1.46/6.29 % ------ no equalities: superposition off
% 1.46/6.29
% 1.46/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.46/6.29
% 1.46/6.29
% 1.46/6.29 % ------
% 1.46/6.29 % Current options:
% 1.46/6.29 % ------
% 1.46/6.29
% 1.46/6.29
% 1.46/6.29 %
% 1.46/6.29
% 1.46/6.29 % ------ Proving...
% 1.46/6.29 %
% 1.46/6.29
% 1.46/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.46/6.29
% 1.46/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.46/6.29
% 1.46/6.29
%------------------------------------------------------------------------------