%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 12:53:09 PM UTC 2026
% Result : Unsatisfiable 13.90s 3.99s
% Output : CNFRefutation 13.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 10
% Syntax : Number of formulae : 92 ( 8 unt; 0 def)
% Number of atoms : 336 ( 2 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 509 ( 265 ~; 244 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 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; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 254 ( 0 sgn 254 !; 0 ?; 241 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
fof(f2,axiom,
! [X0] :
( d2(X0)
| d1(X0)
| c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
fof(f3,axiom,
! [X0] :
( ~ d1(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
fof(f4,axiom,
! [X0] :
( ~ d2(X0)
| ~ c(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
fof(f5,axiom,
! [X0] :
( ~ d2(X0)
| ~ d1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_d1_d2) ).
fof(f7,axiom,
d1(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d1_not_empty) ).
fof(f8,axiom,
d2(a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d2_not_empty) ).
fof(f9,negated_conjecture,
! [X0,X1] :
( ~ c(X1)
| ~ c(X0)
| d1(f(X0,X1))
| d2(f(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
fof(f10,negated_conjecture,
! [X0,X1] :
( ~ d1(X1)
| ~ d1(X0)
| c(f(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
fof(f11,negated_conjecture,
! [X0,X1] :
( ~ d2(X1)
| ~ d2(X0)
| c(f(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_3) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] : f(f(X0,X1),X2) = f(X0,f(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,plain,
! [X0: $i] :
( d2(X0)
| d1(X0)
| c(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,plain,
! [X0: $i] :
( ~ d1(X0)
| ~ c(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,plain,
! [X0: $i] :
( ~ d2(X0)
| ~ c(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i] :
( ~ d2(X0)
| ~ d1(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
d1(a2),
inference(cnf_transformation,[],[f7]) ).
tcf(c_67,plain,
d2(a3),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,negated_conjecture,
! [X0: $i,X1: $i] :
( d2(f(X0,X1))
| d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i] :
( c(f(X0,X1))
| ~ d1(X1)
| ~ d1(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
! [X0: $i,X1: $i] :
( c(f(X0,X1))
| ~ d2(X1)
| ~ d2(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_167,negated_conjecture,
! [X0: $i,X1: $i] :
( c(f(X0,X1))
| ~ d2(X1)
| ~ d2(X0) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_168,negated_conjecture,
! [X0: $i,X1: $i] :
( c(f(X0,X1))
| ~ d1(X1)
| ~ d1(X0) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_169,negated_conjecture,
! [X0: $i,X1: $i] :
( d2(f(X0,X1))
| d1(f(X0,X1))
| ~ c(X1)
| ~ c(X0) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i] :
( ~ d1(X1)
| ~ d1(X0)
| ~ d1(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_168,c_62]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] :
( ~ d2(X1)
| ~ d2(X0)
| ~ d1(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_167,c_62]) ).
tcf(c_380,plain,
! [X0: $i,X1: $i] :
( ~ d1(X1)
| ~ d1(X0)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_168,c_63]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] :
( ~ d2(X1)
| ~ d2(X0)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_167,c_63]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i,X2: $i] :
( d2(f(X0,f(X1,X2)))
| d1(f(f(X0,X1),X2))
| ~ c(X2)
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_60,c_169]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( c(f(X0,f(X1,X2)))
| ~ d2(X2)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_60,c_167]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d2(f(X0,X1))
| ~ d1(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_60,c_367]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d2(f(X0,X1))
| ~ d2(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_60,c_381]) ).
tcf(c_504,plain,
! [X0: $i,X1: $i,X2: $i] :
( d2(f(X0,f(X1,X2)))
| d1(f(X0,f(X1,X2)))
| ~ c(X2)
| ~ c(f(X0,X1)) ),
inference(demodulation,[status(thm)],[c_395,c_60]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X0,f(X1,X2)))
| ~ d2(X0)
| ~ c(X2)
| ~ d2(f(X1,X2))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_504,c_381]) ).
tcf(c_520,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X0,f(X1,X2)))
| ~ d1(X0)
| ~ c(X2)
| ~ d1(f(X1,X2))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_504,c_380]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i] :
( ~ d2(f(X0,X1))
| ~ d1(f(X0,X1)) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_622,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X2,f(X0,X1)))
| ~ d2(X1)
| ~ c(X2)
| ~ d2(f(X2,X0))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_457]) ).
tcf(c_681,plain,
! [X0: $i,X1: $i] :
( d2(f(X0,X1))
| d1(f(X0,X1))
| c(f(X0,X1)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X1)
| ~ c(X2)
| ~ d2(f(X2,X0))
| ~ c(f(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_622,c_428]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d2(X1)
| ~ c(X0)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_167,c_863]) ).
tcf(c_878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d2(X2)
| ~ c(X3)
| ~ d2(f(X3,X0))
| ~ d2(f(X1,X2))
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_397,c_863]) ).
tcf(c_935,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X0,X1))
| c(f(X0,X1))
| ~ d2(X2)
| ~ d2(X1)
| ~ c(X0) ),
inference(superposition,[status(thm)],[c_61,c_877]) ).
tcf(c_983,plain,
! [X0: $i,X1: $i] :
( d1(f(X0,X1))
| c(f(X0,X1))
| ~ d2(X1)
| ~ c(X0) ),
inference(superposition,[status(thm)],[c_67,c_935]) ).
tcf(c_1093,plain,
! [X0: $i,X1: $i] :
( c(f(X0,X1))
| ~ d2(X1)
| ~ c(X0)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_983,c_64]) ).
tcf(c_1241,plain,
! [X0: $i,X1: $i] :
( ~ d2(f(X0,X1))
| ~ c(f(X0,X1)) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1479,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( d1(f(X3,X0))
| ~ d2(X1)
| ~ c(X3)
| ~ c(X2)
| ~ c(X0)
| ~ d2(f(X2,X3))
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_878]) ).
tcf(c_1521,plain,
! [X0: $i,X1: $i] :
( ~ d2(f(X0,X1))
| ~ c(X0)
| ~ d2(X1) ),
inference(global_subsumption_just,[status(thm)],[c_1479,c_1093,c_1241]) ).
tcf(c_1522,plain,
! [X0: $i,X1: $i] :
( ~ d2(X1)
| ~ c(X0)
| ~ d2(f(X0,X1)) ),
inference(renaming,[status(thm)],[c_1521]) ).
tcf(c_1589,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X0)
| ~ c(X2)
| ~ d2(f(X1,X2))
| ~ c(f(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_519,c_367]) ).
tcf(c_1603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d2(X0)
| ~ c(X1)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_167,c_1589]) ).
tcf(c_1608,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ c(X3)
| ~ d2(f(X2,X3))
| ~ d2(f(X0,X1))
| ~ c(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_60,c_1589]) ).
tcf(c_1667,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X1,X0))
| c(f(X1,X0))
| ~ d2(X2)
| ~ d2(X1)
| ~ c(X0) ),
inference(superposition,[status(thm)],[c_61,c_1603]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i] :
( d1(f(X1,X0))
| c(f(X1,X0))
| ~ d2(X1)
| ~ c(X0) ),
inference(superposition,[status(thm)],[c_67,c_1667]) ).
tcf(c_2366,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d1(X0)
| ~ c(X2)
| ~ d1(f(X1,X2))
| ~ c(f(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_520,c_366]) ).
tcf(c_2379,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d1(X2)
| ~ d1(X0)
| ~ c(X1)
| ~ d1(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_168,c_2366]) ).
tcf(c_4415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d1(X2)
| ~ c(X3)
| ~ d2(f(X2,X0))
| ~ d2(f(X1,X3))
| ~ d1(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_168,c_1608]) ).
tcf(c_4936,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c(f(X3,X0))
| ~ d2(X3)
| ~ d1(X2)
| ~ c(X1)
| ~ c(X0)
| ~ d2(f(X2,X3))
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_1730,c_4415]) ).
tcf(c_16014,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d2(X3)
| ~ d1(X2)
| ~ c(X1)
| ~ c(X0)
| ~ d2(f(X2,X3))
| ~ d2(f(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4936,c_1589]) ).
tcf(c_16034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( d1(f(X2,X3))
| ~ d2(X1)
| ~ d1(X0)
| ~ c(X3)
| ~ c(X2)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_16014]) ).
tcf(c_16142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( d1(f(X2,X3))
| ~ d2(X1)
| ~ d2(f(X0,X1))
| ~ c(X2)
| ~ c(X3) ),
inference(global_subsumption_just,[status(thm)],[c_16034,c_61,c_70,c_561,c_983,c_1241,c_16034]) ).
tcf(c_16143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( d1(f(X2,X3))
| ~ d2(X1)
| ~ c(X3)
| ~ c(X2)
| ~ d2(f(X0,X1)) ),
inference(renaming,[status(thm)],[c_16142]) ).
tcf(c_16159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( d1(f(X3,X4))
| ~ d2(X2)
| ~ c(X4)
| ~ c(X3)
| ~ d2(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_60,c_16143]) ).
tcf(c_16211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( d1(f(X3,X4))
| d1(f(X2,f(X0,X1)))
| ~ d2(X1)
| ~ c(X4)
| ~ c(X3)
| ~ c(X2)
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_16159]) ).
tcf(c_18312,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X2,f(X0,X1)))
| ~ d2(X1)
| ~ c(X2)
| ~ c(f(X0,X1)) ),
inference(equality_factoring,[status(thm)],[c_16211]) ).
tcf(c_18448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( d1(f(X0,f(X1,f(X2,X3))))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_60,c_18312]) ).
tcf(c_19729,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ d2(X2)
| ~ d1(X4)
| ~ d1(X3)
| ~ c(f(X3,X0))
| ~ c(f(X1,X2))
| ~ c(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_18448,c_2379]) ).
tcf(c_28684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ d2(X1)
| ~ d1(X4)
| ~ d1(X2)
| ~ d2(f(X3,X0))
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_397,c_19729]) ).
tcf(c_28949,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ d2(X4)
| ~ d2(X2)
| ~ d1(X3)
| ~ d1(X0)
| ~ d2(f(X1,X2))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_167,c_28684]) ).
tcf(c_29883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ d2(X4)
| ~ d2(X1)
| ~ d1(X3)
| ~ d1(X2)
| ~ d1(X0)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_168,c_28949]) ).
tcf(c_29884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ d2(X4)
| ~ d2(X2)
| ~ d2(X1)
| ~ d2(X0)
| ~ d1(X3)
| ~ d1(X2)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_167,c_28949]) ).
tcf(c_30131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ d2(X4)
| ~ d2(X1)
| ~ d1(X3)
| ~ d1(X2)
| ~ d2(f(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_29883,c_61,c_381,c_1522,c_29883]) ).
tcf(c_30143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( d1(f(X4,X2))
| c(f(X4,X2))
| ~ d2(X3)
| ~ d2(X2)
| ~ d1(X1)
| ~ d1(X0) ),
inference(superposition,[status(thm)],[c_61,c_30131]) ).
tcf(c_30280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( d1(f(X3,X1))
| c(f(X3,X1))
| ~ d2(X2)
| ~ d2(X1)
| ~ d1(X0) ),
inference(superposition,[status(thm)],[c_66,c_30143]) ).
tcf(c_30323,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X2,X0))
| c(f(X2,X0))
| ~ d2(X1)
| ~ d2(X0) ),
inference(superposition,[status(thm)],[c_66,c_30280]) ).
tcf(c_30363,plain,
! [X0: $i,X1: $i] :
( d1(f(X1,X0))
| c(f(X1,X0))
| ~ d2(X0) ),
inference(superposition,[status(thm)],[c_67,c_30323]) ).
tcf(c_30381,plain,
! [X0: $i,X1: $i] :
( c(f(X0,X1))
| ~ d2(X1)
| ~ d2(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_30363,c_64]) ).
tcf(c_30851,plain,
! [X0: $i,X1: $i] :
( ~ d2(X1)
| ~ d2(f(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_29884,c_1241,c_30381]) ).
tcf(c_30862,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d2(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_60,c_30851]) ).
tcf(c_30883,plain,
! [X0: $i,X1: $i,X2: $i] :
( d1(f(X1,f(X2,X0)))
| c(f(X1,f(X2,X0)))
| ~ d2(X0) ),
inference(superposition,[status(thm)],[c_61,c_30862]) ).
tcf(c_31591,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c(f(X2,f(X0,X1)))
| ~ d2(X1)
| ~ d1(X3)
| ~ d1(X2)
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_30883,c_2379]) ).
tcf(c_31597,plain,
! [X0: $i,X1: $i,X2: $i] :
( c(f(X2,f(X0,X1)))
| ~ d2(X1)
| ~ d1(X2)
| ~ d1(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_30883,c_366]) ).
tcf(c_33436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c(f(X2,f(X0,X1)))
| ~ d2(X1)
| ~ d1(X3)
| ~ d1(X2) ),
inference(global_subsumption_just,[status(thm)],[c_31591,c_681,c_30851,c_31597,c_31591]) ).
tcf(c_33437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c(f(X0,f(X3,X2)))
| ~ d2(X2)
| ~ d1(X1)
| ~ d1(X0) ),
inference(renaming,[status(thm)],[c_33436]) ).
tcf(c_33452,plain,
! [X0: $i,X1: $i,X2: $i] :
( c(f(X0,f(X2,X1)))
| ~ d2(X1)
| ~ d1(X0) ),
inference(superposition,[status(thm)],[c_66,c_33437]) ).
tcf(c_33560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d1(X0)
| ~ d1(f(X0,f(X1,X2))) ),
inference(superposition,[status(thm)],[c_33452,c_62]) ).
tcf(c_33879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d2(X3)
| ~ d1(X0)
| ~ d1(f(X0,f(X1,f(X2,X3)))) ),
inference(superposition,[status(thm)],[c_60,c_33560]) ).
tcf(c_34414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d2(X3)
| ~ d1(X0)
| ~ c(f(X2,X3))
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_18448,c_33879]) ).
tcf(c_36968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d2(X1)
| ~ d1(X3)
| ~ d1(X2)
| ~ c(f(X0,X1)) ),
inference(superposition,[status(thm)],[c_168,c_34414]) ).
tcf(c_37164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ d2(X3)
| ~ d2(X2)
| ~ d1(X1)
| ~ d1(X0) ),
inference(superposition,[status(thm)],[c_167,c_36968]) ).
tcf(c_37322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ d2(X2)
| ~ d2(X1)
| ~ d1(X0) ),
inference(superposition,[status(thm)],[c_66,c_37164]) ).
tcf(c_37410,plain,
! [X0: $i,X1: $i] :
( ~ d2(X1)
| ~ d2(X0) ),
inference(superposition,[status(thm)],[c_66,c_37322]) ).
tcf(c_37557,plain,
! [X0: $i] : ~ d2(X0),
inference(superposition,[status(thm)],[c_67,c_37410]) ).
tcf(c_37562,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_67,c_37557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.41 % Computer : n005.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 04:31:17 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 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
% 0.14/0.49
% 0.14/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.49
% 0.14/0.49 % Detected problem language: tptp
% 0.21/0.51 % Proving...
% 13.90/3.99 % SZS status Started for theBenchmark.p
% 13.90/3.99 % SZS status Unsatisfiable for theBenchmark.p
% 13.90/3.99
% 13.90/3.99 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 13.90/3.99
% 13.90/3.99 % ------ iProver source info
% 13.90/3.99
% 13.90/3.99 % git: date: 2026-07-19 20:42:38 +0200
% 13.90/3.99 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 13.90/3.99 % git: non_committed_changes: false
% 13.90/3.99
% 13.90/3.99 % ------ Parsing...% successful
% 13.90/3.99
% 13.90/3.99
% 13.90/3.99 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 13.90/3.99
% 13.90/3.99 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 13.90/3.99
% 13.90/3.99 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 13.90/3.99
% 13.90/3.99 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 13.90/3.99 % ------ Proving...
% 13.90/3.99 % ------ Problem Properties
% 13.90/3.99
% 13.90/3.99 %
% 13.90/3.99 % clauses 11
% 13.90/3.99 % conjectures 3
% 13.90/3.99 % EPR 7
% 13.90/3.99 % Horn 9
% 13.90/3.99 % unary 4
% 13.90/3.99 % binary 3
% 13.90/3.99 % lits 23
% 13.90/3.99 % lits eq 1
% 13.90/3.99 % fd_pure 0
% 13.90/3.99 % fd_pseudo 0
% 13.90/3.99 % fd_cond 0
% 13.90/3.99 % fd_pseudo_cond 0
% 13.90/3.99 % AC symbols 0
% 13.90/3.99
% 13.90/3.99 % ------ Schedule dynamic 5 is on
% 13.90/3.99
% 13.90/3.99 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 13.90/3.99
% 13.90/3.99
% 13.90/3.99 % ------
% 13.90/3.99 % Current options:
% 13.90/3.99 % ------
% 13.90/3.99
% 13.90/3.99
% 13.90/3.99 %
% 13.90/3.99
% 13.90/3.99 % ------ Proving...
% 13.90/3.99 %
% 13.90/3.99
% 13.90/3.99 % SZS status Unsatisfiable for theBenchmark.p
% 13.90/3.99
% 13.90/3.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.90/3.99
% 13.90/3.99
%------------------------------------------------------------------------------