%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : ITP069^1 : TPTP v9.2.0. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 07:51:09 PM UTC 2025 % Result : Theorem 3.74s 3.90s % Output : Proof 3.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ITP069^1 : TPTP v9.2.0. Released v7.5.0. % 0.07/0.13 % Command : duper %s % 0.13/0.34 % Computer : n006.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 00:21:53 EDT 2025 % 0.13/0.34 % CPUTime : % 3.74/3.90 SZS status Theorem for theBenchmark.p % 3.74/3.90 SZS output start Proof for theBenchmark.p % 3.74/3.90 Clause #0 (by assumption #[]): Eq (is_heap_a (heapIm970322378pify_a r)) True % 3.74/3.90 Clause #1 (by assumption #[]): Eq (is_heap_a (heapIm970322378pify_a l)) True % 3.74/3.90 Clause #2 (by assumption #[]): Eq % 3.74/3.90 (is_heap_a (heapIm970322378pify_a l) → % 3.74/3.90 is_heap_a (heapIm970322378pify_a r) → % 3.74/3.90 Eq (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) % 3.74/3.90 (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) → % 3.74/3.90 is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) % 3.74/3.90 True % 3.74/3.90 Clause #3 (by assumption #[]): Eq % 3.74/3.90 (∀ (V : a) (L R : tree_a), % 3.74/3.90 Eq (heapIm970322378pify_a (t_a V L R)) % 3.74/3.90 (heapIm1091024090Down_a (t_a V (heapIm970322378pify_a L) (heapIm970322378pify_a R)))) % 3.74/3.90 True % 3.74/3.90 Clause #134 (by assumption #[]): Eq (Not (is_heap_a (heapIm970322378pify_a (t_a v l r)))) True % 3.74/3.90 Clause #137 (by clausification #[2]): Or (Eq (is_heap_a (heapIm970322378pify_a l)) False) % 3.74/3.90 (Eq % 3.74/3.90 (is_heap_a (heapIm970322378pify_a r) → % 3.74/3.90 Eq (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) % 3.74/3.90 (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) → % 3.74/3.90 is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) % 3.74/3.90 True) % 3.74/3.90 Clause #138 (by clausification #[137]): Or (Eq (is_heap_a (heapIm970322378pify_a l)) False) % 3.74/3.90 (Or (Eq (is_heap_a (heapIm970322378pify_a r)) False) % 3.74/3.90 (Eq % 3.74/3.90 (Eq (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) % 3.74/3.90 (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) → % 3.74/3.90 is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) % 3.74/3.90 True)) % 3.74/3.90 Clause #139 (by clausification #[138]): Or (Eq (is_heap_a (heapIm970322378pify_a l)) False) % 3.74/3.90 (Or (Eq (is_heap_a (heapIm970322378pify_a r)) False) % 3.74/3.90 (Or % 3.74/3.90 (Eq % 3.74/3.90 (Eq (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) % 3.74/3.90 (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r))) % 3.74/3.90 False) % 3.74/3.90 (Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True))) % 3.74/3.90 Clause #140 (by clausification #[139]): Or (Eq (is_heap_a (heapIm970322378pify_a l)) False) % 3.74/3.90 (Or (Eq (is_heap_a (heapIm970322378pify_a r)) False) % 3.74/3.90 (Or (Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True) % 3.74/3.90 (Ne (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)) % 3.74/3.90 (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r))))) % 3.74/3.90 Clause #141 (by eliminate resolved literals #[140]): Or (Eq (is_heap_a (heapIm970322378pify_a l)) False) % 3.74/3.90 (Or (Eq (is_heap_a (heapIm970322378pify_a r)) False) % 3.74/3.90 (Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True)) % 3.74/3.90 Clause #142 (by forward demodulation #[141, 1]): Or (Eq True False) % 3.74/3.90 (Or (Eq (is_heap_a (heapIm970322378pify_a r)) False) % 3.74/3.90 (Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True)) % 3.74/3.90 Clause #143 (by clausification #[142]): Or (Eq (is_heap_a (heapIm970322378pify_a r)) False) % 3.74/3.90 (Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True) % 3.74/3.90 Clause #144 (by forward demodulation #[143, 0]): Or (Eq True False) % 3.74/3.90 (Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True) % 3.74/3.90 Clause #145 (by clausification #[144]): Eq (is_heap_a (heapIm1091024090Down_a (t_a v (heapIm970322378pify_a l) (heapIm970322378pify_a r)))) True % 3.74/3.90 Clause #178 (by clausification #[3]): ∀ (a : a), % 3.74/3.90 Eq % 3.74/3.90 (∀ (L R : tree_a), % 3.74/3.90 Eq (heapIm970322378pify_a (t_a a L R)) % 3.74/3.90 (heapIm1091024090Down_a (t_a a (heapIm970322378pify_a L) (heapIm970322378pify_a R)))) % 3.74/3.90 True % 3.74/3.90 Clause #179 (by clausification #[178]): ∀ (a : a) (a_1 : tree_a), % 3.74/3.90 Eq % 3.74/3.90 (∀ (R : tree_a), % 3.74/3.90 Eq (heapIm970322378pify_a (t_a a a_1 R)) % 3.74/3.90 (heapIm1091024090Down_a (t_a a (heapIm970322378pify_a a_1) (heapIm970322378pify_a R)))) % 3.74/3.90 True % 3.74/3.90 Clause #180 (by clausification #[179]): ∀ (a : a) (a_1 a_2 : tree_a), % 3.74/3.90 Eq % 3.74/3.90 (Eq (heapIm970322378pify_a (t_a a a_1 a_2)) % 3.74/3.90 (heapIm1091024090Down_a (t_a a (heapIm970322378pify_a a_1) (heapIm970322378pify_a a_2)))) % 3.74/3.90 True % 3.74/3.90 Clause #181 (by clausification #[180]): ∀ (a : a) (a_1 a_2 : tree_a), % 3.74/3.90 Eq (heapIm970322378pify_a (t_a a a_1 a_2)) % 3.74/3.90 (heapIm1091024090Down_a (t_a a (heapIm970322378pify_a a_1) (heapIm970322378pify_a a_2))) % 3.74/3.90 Clause #182 (by backward demodulation #[181, 145]): Eq (is_heap_a (heapIm970322378pify_a (t_a v l r))) True % 3.74/3.90 Clause #352 (by clausification #[134]): Eq (is_heap_a (heapIm970322378pify_a (t_a v l r))) False % 3.74/3.90 Clause #353 (by superposition #[352, 182]): Eq False True % 3.74/3.90 Clause #382 (by clausification #[353]): False % 3.74/3.90 SZS output end Proof for theBenchmark.p 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