%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:38:17 PM UTC 2026
% Result : Unsatisfiable 2.82s 1.27s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 127 ( 98 unt; 5 def)
% Number of atoms : 466 ( 127 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 142 ( 73 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-1 aty)
% Number of variables : 182 ( 0 sgn 182 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',associativity_of_multiplication2) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/RNG001-0.ax',addition_is_well_defined) ).
fof(f19,axiom,
! [X0] : product(multiplicative_identity,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_multiplicative_identity) ).
fof(f24,axiom,
! [X2,X0,X1] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_symmetry) ).
fof(f25,negated_conjecture,
sum(b,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_c) ).
fof(f26,negated_conjecture,
product(d,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_plus_a) ).
fof(f27,negated_conjecture,
product(b,a,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_plus_a) ).
fof(f28,negated_conjecture,
product(c,a,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_plus_a) ).
fof(f29,negated_conjecture,
~ sum(l,n,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
tcf(c_76,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_77,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_81,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( product(X2,X5,X4)
| ~ product(X1,X5,X3)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_94,plain,
! [X0: $i] : product(multiplicative_identity,X0,X0),
inference(cnf_transformation,[],[f19]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_98,negated_conjecture,
sum(b,c,d),
inference(cnf_transformation,[],[f25]) ).
tcf(c_99,negated_conjecture,
product(d,a,additive_identity),
inference(cnf_transformation,[],[f26]) ).
tcf(c_100,negated_conjecture,
product(b,a,l),
inference(cnf_transformation,[],[f27]) ).
tcf(c_101,negated_conjecture,
product(c,a,n),
inference(cnf_transformation,[],[f28]) ).
tcf(c_102,negated_conjecture,
~ sum(l,n,additive_identity),
inference(cnf_transformation,[],[f29]) ).
tcf(c_105,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_113,plain,
( ( additive_identity = additive_identity )
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_115,plain,
! [X0: $i] : multiply(multiplicative_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_94]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X0) = X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_97]) ).
tcf(c_120,plain,
add(b,c) = d,
inference(well_definedness,[status(thm)],[c_98]) ).
tcf(c_121,plain,
multiply(d,a) = additive_identity,
inference(well_definedness,[status(thm)],[c_99]) ).
tcf(c_122,plain,
multiply(b,a) = l,
inference(well_definedness,[status(thm)],[c_100]) ).
tcf(c_123,plain,
multiply(c,a) = n,
inference(well_definedness,[status(thm)],[c_101]) ).
tcf(c_124,plain,
add(l,n) != additive_identity,
inference(well_definedness,[status(thm)],[c_102]) ).
tcf(c_125,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_126,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_77]) ).
tcf(c_130,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_81]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_83]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_84]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X2,X5) = X4 )
| ( multiply(X1,X5) != X3 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X5,X1) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X0,X3) != X5 )
| ( multiply(X3,X1) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_135]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(unflattening,[status(thm)],[c_118]) ).
tcf(c_300,plain,
multiply(a,b) = l,
inference(demodulation,[status(thm)],[c_122,c_298]) ).
tcf(c_301,plain,
multiply(a,c) = n,
inference(demodulation,[status(thm)],[c_123,c_298]) ).
tcf(c_302,plain,
multiply(a,d) = additive_identity,
inference(demodulation,[status(thm)],[c_121,c_298]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(unflattening,[status(thm)],[c_139]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_133]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_147]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_143]) ).
tcf(c_363,definition,
iPr_def_10 = multiply(a,d),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_364,definition,
iPr_def_11 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_365,definition,
iPr_def_12 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_366,definition,
iPr_def_13 = add(l,n),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_367,definition,
iPr_def_14 = add(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_368,plain,
iPr_def_10 = additive_identity,
inference(demodulation,[status(thm)],[c_302,c_363]) ).
tcf(c_369,plain,
iPr_def_11 = n,
inference(demodulation,[status(thm)],[c_301,c_364]) ).
tcf(c_370,plain,
iPr_def_12 = l,
inference(demodulation,[status(thm)],[c_300,c_365]) ).
tcf(c_371,plain,
iPr_def_13 != additive_identity,
inference(demodulation,[status(thm)],[c_124,c_366]) ).
tcf(c_372,plain,
iPr_def_14 = d,
inference(demodulation,[status(thm)],[c_120,c_367]) ).
tcf(c_373,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_451,plain,
! [X0: $i] : add(iPr_def_10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_125,c_368]) ).
tcf(c_459,plain,
multiply(a,iPr_def_14) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_363,c_372]) ).
tcf(c_460,plain,
multiply(iPr_def_14,a) = iPr_def_10,
inference(demodulation,[status(thm)],[c_459,c_298]) ).
tcf(c_461,plain,
add(iPr_def_12,iPr_def_11) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_366,c_369,c_370]) ).
tcf(c_462,plain,
add(iPr_def_11,iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_461,c_296]) ).
tcf(c_463,plain,
! [X0: $i] : add(X0,iPr_def_10) = X0,
inference(light_normalisation,[status(thm)],[c_126,c_368]) ).
tcf(c_464,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_130,c_368]) ).
tcf(c_676,plain,
! [X0: $i] :
( ( iPr_def_13 = additive_identity )
| ( iPr_def_13 != X0 )
| ( additive_identity != X0 ) ),
inference(instantiation,[status(thm)],[c_374]) ).
tcf(c_679,plain,
iPr_def_13 = iPr_def_13,
inference(instantiation,[status(thm)],[c_373]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_374]) ).
tcf(c_690,plain,
! [X0: $i] :
( ( iPr_def_13 = X0 )
| ( iPr_def_13 != iPr_def_13 )
| ( X0 != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_807,plain,
! [X0: $i] : add(b,add(c,X0)) = add(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_367,c_307]) ).
tcf(c_808,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(iPr_def_10,X1),
inference(superposition,[status(thm)],[c_464,c_307]) ).
tcf(c_811,plain,
! [X0: $i] : add(iPr_def_11,add(iPr_def_12,X0)) = add(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_462,c_307]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_808,c_451]) ).
tcf(c_867,plain,
! [X0: $i] : add(X0,iPr_def_10) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_464,c_863]) ).
tcf(c_868,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_296,c_863]) ).
tcf(c_878,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_867,c_463]) ).
tcf(c_888,plain,
( ( iPr_def_13 = add(additive_identity,iPr_def_13) )
| ( iPr_def_13 != iPr_def_13 )
| ( add(additive_identity,iPr_def_13) != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_690]) ).
tcf(c_889,plain,
add(additive_identity,iPr_def_13) = iPr_def_13,
inference(instantiation,[status(thm)],[c_125]) ).
tcf(c_1169,plain,
add(iPr_def_14,additive_inverse(b)) = c,
inference(superposition,[status(thm)],[c_807,c_868]) ).
tcf(c_1197,plain,
! [X0: $i] : add(iPr_def_14,add(additive_inverse(b),X0)) = add(c,X0),
inference(superposition,[status(thm)],[c_1169,c_307]) ).
tcf(c_1276,plain,
( ( iPr_def_13 = additive_identity )
| ( iPr_def_13 != add(additive_identity,iPr_def_13) )
| ( additive_identity != add(additive_identity,iPr_def_13) ) ),
inference(instantiation,[status(thm)],[c_676]) ).
tcf(c_1299,plain,
! [X0: $i] : add(iPr_def_11,add(iPr_def_12,X0)) = add(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_811,c_296]) ).
tcf(c_1534,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = multiply(iPr_def_10,X1),
inference(superposition,[status(thm)],[c_464,c_309]) ).
tcf(c_1537,plain,
! [X0: $i,X1: $i] : add(multiply(iPr_def_10,X0),multiply(X1,X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_451,c_309]) ).
tcf(c_1745,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = multiply(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_464,c_311]) ).
tcf(c_1956,plain,
! [X0: $i] : add(multiply(iPr_def_10,X0),X0) = X0,
inference(superposition,[status(thm)],[c_115,c_1537]) ).
tcf(c_1991,plain,
! [X0: $i] : add(X0,multiply(iPr_def_10,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_1956,c_305,c_298,c_307,c_296]) ).
tcf(c_2438,plain,
! [X0: $i] : add(X0,multiply(additive_inverse(multiplicative_identity),X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_115,c_1534]) ).
tcf(c_2446,plain,
add(iPr_def_10,multiply(additive_inverse(iPr_def_14),a)) = multiply(iPr_def_10,a),
inference(superposition,[status(thm)],[c_460,c_1534]) ).
tcf(c_2481,plain,
add(iPr_def_10,multiply(a,additive_inverse(iPr_def_14))) = multiply(iPr_def_10,a),
inference(theory_normalisation,[status(thm)],[c_2446,c_305,c_298,c_307,c_296]) ).
tcf(c_2652,plain,
add(iPr_def_12,multiply(a,additive_inverse(b))) = multiply(a,iPr_def_10),
inference(superposition,[status(thm)],[c_365,c_1745]) ).
tcf(c_2689,plain,
add(iPr_def_12,multiply(a,additive_inverse(b))) = multiply(iPr_def_10,a),
inference(theory_normalisation,[status(thm)],[c_2652,c_305,c_298,c_307,c_296]) ).
tcf(c_2798,plain,
! [X0: $i,X1: $i] :
( ( X1 = add(additive_identity,iPr_def_13) )
| ( X1 != X0 )
| ( add(additive_identity,iPr_def_13) != X0 ) ),
inference(instantiation,[status(thm)],[c_374]) ).
tcf(c_2799,plain,
( ( additive_identity = add(additive_identity,iPr_def_13) )
| ( additive_identity != additive_identity )
| ( add(additive_identity,iPr_def_13) != additive_identity ) ),
inference(instantiation,[status(thm)],[c_2798]) ).
tcf(c_3446,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = multiply(iPr_def_10,additive_inverse(X0)),
inference(superposition,[status(thm)],[c_1991,c_863]) ).
tcf(c_3452,plain,
! [X0: $i] : multiply(iPr_def_10,additive_inverse(X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_3446,c_464]) ).
tcf(c_3695,plain,
! [X0: $i] : multiply(iPr_def_10,X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_878,c_3452]) ).
tcf(c_3881,plain,
add(iPr_def_12,multiply(a,additive_inverse(b))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2689,c_3695]) ).
tcf(c_3884,plain,
! [X0: $i] : add(iPr_def_12,add(multiply(a,additive_inverse(b)),X0)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_3881,c_307]) ).
tcf(c_3891,plain,
! [X0: $i] : add(iPr_def_12,add(multiply(a,additive_inverse(b)),X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3884,c_451]) ).
tcf(c_4224,plain,
! [X0: $i] : add(iPr_def_12,add(X0,multiply(a,additive_inverse(b)))) = X0,
inference(superposition,[status(thm)],[c_296,c_3891]) ).
tcf(c_4398,plain,
! [X0: $i] : add(iPr_def_11,add(X0,iPr_def_12)) = add(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_296,c_1299]) ).
tcf(c_5064,plain,
! [X0: $i] : add(X0,multiply(additive_inverse(multiplicative_identity),X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2438,c_3695]) ).
tcf(c_5085,plain,
! [X0: $i] : multiply(additive_inverse(multiplicative_identity),additive_inverse(X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_5064,c_863]) ).
tcf(c_5091,plain,
! [X0: $i] : multiply(additive_inverse(multiplicative_identity),additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_5085,c_463]) ).
tcf(c_5143,plain,
! [X0: $i] : multiply(additive_inverse(multiplicative_identity),X0) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_878,c_5091]) ).
tcf(c_5176,plain,
! [X0: $i] : multiply(X0,additive_inverse(multiplicative_identity)) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_5143,c_298]) ).
tcf(c_5621,plain,
multiply(a,additive_inverse(iPr_def_14)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2481,c_451,c_3695]) ).
tcf(c_6817,plain,
! [X0: $i] : add(iPr_def_14,add(multiply(b,additive_inverse(multiplicative_identity)),X0)) = add(c,X0),
inference(demodulation,[status(thm)],[c_1197,c_5176]) ).
tcf(c_6837,plain,
multiply(b,additive_inverse(multiplicative_identity)) = add(c,additive_inverse(iPr_def_14)),
inference(superposition,[status(thm)],[c_6817,c_868]) ).
tcf(c_7170,plain,
! [X0: $i] : add(iPr_def_12,add(X0,iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_4224,c_311,c_364,c_463,c_5176,c_5621,c_6837]) ).
tcf(c_7171,plain,
! [X0: $i] : add(iPr_def_11,add(X0,iPr_def_12)) = X0,
inference(theory_normalisation,[status(thm)],[c_7170,c_305,c_298,c_307,c_296]) ).
tcf(c_7173,plain,
! [X0: $i] : add(X0,iPr_def_13) = X0,
inference(demodulation,[status(thm)],[c_4398,c_7171]) ).
tcf(c_7189,plain,
add(additive_identity,iPr_def_13) = additive_identity,
inference(instantiation,[status(thm)],[c_7173]) ).
tcf(c_7190,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7189,c_2799,c_1276,c_889,c_888,c_679,c_371,c_113,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG040-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 07:55:41 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 2.82/1.27 % SZS status Started for theBenchmark.p
% 2.82/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.82/1.27
% 2.82/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.82/1.27
% 2.82/1.27 % ------ iProver source info
% 2.82/1.27
% 2.82/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.82/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.82/1.27 % git: non_committed_changes: false
% 2.82/1.27
% 2.82/1.27 % ------ Parsing...% successful
% 2.82/1.27
% 2.82/1.27
% 2.82/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.82/1.27
% 2.82/1.27 % ------ Preprocessing... sup_sim: 21 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.82/1.27
% 2.82/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.82/1.27
% 2.82/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.82/1.27 % ------ Proving...
% 2.82/1.27 % ------ Problem Properties
% 2.82/1.27
% 2.82/1.27 %
% 2.82/1.27 % clauses 22
% 2.82/1.27 % conjectures 0
% 2.82/1.27 % EPR 5
% 2.82/1.27 % Horn 21
% 2.82/1.27 % unary 21
% 2.82/1.27 % binary 1
% 2.82/1.27 % lits 23
% 2.82/1.27 % lits eq 23
% 2.82/1.27 % fd_pure 0
% 2.82/1.27 % fd_pseudo 0
% 2.82/1.27 % fd_cond 1
% 2.82/1.27 % fd_pseudo_cond 0
% 2.82/1.27 % AC symbols 2
% 2.82/1.27
% 2.82/1.27 % ------ Schedule dynamic 5 is on
% 2.82/1.27
% 2.82/1.27 % ------ no conjectures: strip conj schedule
% 2.82/1.27
% 2.82/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.82/1.27
% 2.82/1.27
% 2.82/1.27 % ------
% 2.82/1.27 % Current options:
% 2.82/1.27 % ------
% 2.82/1.27
% 2.82/1.27
% 2.82/1.27 %
% 2.82/1.27
% 2.82/1.27 % ------ Proving...
% 2.82/1.27 %
% 2.82/1.27
% 2.82/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.82/1.27
% 2.82/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.82/1.27
% 2.82/1.27
%------------------------------------------------------------------------------